local spectral gap in simple lie groups and applications we introduce a novel notion of local spectral gap for general possibly infinite measure preserving actions we establish local spectral gap for the left translation action gamma curvearrowright g whenever gamma is a dense subgroup generated by algebraic elements of an arbitrary connected simple lie group g this extends to the non compact setting works of bourgain and gamburd invent math 171 83 121 2008 j eur math soc jems 14 1455 1511 2012 and benoist and de saxce invent math 205 337 361 2016 we present several applications to the banach ruziewicz problem orbit equivalence rigidity continuous and monotone expanders and bounded random walks on g in particular we prove that up to a multiplicative constant the haar measure is the unique gamma invariant finitely additive measure defined on all bounded measurable subsets of g

a class of superrigid group von neumann algebras we prove that for any group g in a fairly large class of generalized wreath product groups the associated von neumann algebra lg completely remembers the group g more precisely if lg is isomorphic to the von neumann algebra l of an arbitrary countable group then must be isomorphic to g this represents the rst superrigidity result pertaining to group von neumann algebras

a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

on subalgebras of the car algebra abstract every nuclear unital separable c algebra a is unitally and completely isometrically ismorphic to the range of a unital completely positive projection on the car algbra b m 2 m 2 let c be a nuclearly imbeddable separable unital c algebra in the sense of voiculescu vo13 then there exists a c subalgebra e of the car algebra b such that c is isomorphic to a quotient c algebra of e we include one of the possible proofs that exact c algebras are nuclearly imbeddable proofs of g covariant analogs are outlined for compact g some related results are obtained on non selfadjoint operator algebras the unital separable nuclear c algebras not of type i are mutually cb isomorphic and have cb distance 256 separable lindenstrauss spaces are isometric to quotients of the car algebra by a sum of closed left and a closed right ideal

orbit equivalence rigidity consider a countable group acting ergodically by measure p reserving transformations on a probability space x and let r be the corresponding orbit equivalence relation on x the following rigidity phenomenon is shown there exist group actions such that the equivalence relation r on x determines the group and the action x uniquely up to finite groups the natural action of sln z on the n torus r n z n for n 2 is one of such examples the interpretation of these results in the context of von neumann algebras provides some support to the conjecture of connes on rigidity of group algebras for groups with property t our rigidity results also give examples of countable equivalence relations of type ii1 which cannot be generated mod 0 by a free action of any group this gives a negative answer to a long standing problem of feldman and moore

w superrigidity for group von neumann algebras of left right wreath products we prove that for many nonamenable groups including all hyperbolic groups and all nontrivial free products the left right wreath product groupg z 2z o is w superrigid this means that the group von neumann algebra lg entirely remembers g more precisely if lg is isomorphic with l for an arbitrary countable group then must be isomorphic withg

some prime factorization results for type ii1 factors we prove several unique prime factorization results for tensor products of type ii1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected lie groups of real rank 1 in particular we show that if mathcal r overline otimes mathcal l mathbb f r 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f r m is isomorphic to a subfactor in mathcal r overline otimes mathcal l mathbb f s 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f s n for some 2 ri sj then m n

cartan subalgebras in c algebras existence and uniqueness we initiate the study of cartan subalgebras in c algebras with a particular focus on existence and uniqueness questions for homogeneous c algebras these questions can be analyzed systematically using the theory of fiber bundles for group c algebras while we are able to find cartan subalgebras in c algebras of many connected lie groups there are classes of discrete groups for instance non abelian free groups whose reduced group c algebras do not have any cartan subalgebras moreover we show that uniqueness of cartan subalgebras usually fails for classifiable c algebras however distinguished cartan subalgebras exist in some cases for instance in nuclear uniform roe algebras

group cocycles and the ring of affiliated operators in this article we study cocycles of discrete countable groups with values in 2 g and the ring of affiliated operators ug we clarify properties of the first cohomology of a group g with coefficients in 2 g and answer several questions from de cornulier et al transform groups 13 1 125 147 2008 moreover we obtain strong results about the existence of free subgroups and the subgroup structure provided the group has a positive first 2 betti num ber we give numerous applications and examples of groups which satisfy our assumptions

dissipativity analysis for discrete stochastic neural networks with markovian delays and partially known transition matrix the problem of dissipativity analysis for a class of discrete time stochastic neural networks with discrete and finite distributed delays is considered in this paper system parameters are described by a discrete time markov chain a discretized jensen inequality and lower bounds lemma are employed to reduce the number of decision variables and to deal with the involved finite sum quadratic terms in an efficient way a sufficient condition is derived to ensure that the neural networks under consideration is globally delay dependent asymptotically stable in the mean square and strictly z s g a dissipative next the case in which the transition probabilities of the markovian channels are partially known is discussed numerical examples are given to emphasize the merits of reduced conservatism of the developed results

unique prime factorization for infinite tensor product factors abstract in this article we investigate a unique prime factorization property for infinite tensor product factors we provide several examples of type ii and iii factors which satisfy this property including all free product factors with diffuse free product components in the type iii setting this is the first classification result for infinite tensor product non amenable factors our proof is based on popa s intertwining techniques and a characterization of relative amenability on the continuous cores

some unique group measure space decomposition results using an approach emerging from the theory of closable deriva tions on von neumann algebras we exhibit a class of groups cr satisfying the following property given any groups 1 2 2 cr then any free ergodic measure preserving action on a probability space 1 2 y x gives rise to a von neumann algebra with unique group measure space cartan subalgebra pairing this result with popa s orbit equivalence superrigidity theorem we obtain new examples of w superrigid actions

three dimensional x projection method with acceleration techniques for solving systems of linear equations abstract the solution of linear systems of equations using a 3 dimensional x projection method is presented at each step of the iterative process the approximate solution vector is projected to a point in the intersection of three of the hyperplanes of the linear system nonsingularity of the coefficient matrix is the only requirement for convergence an algorithm is presented to select triples of hyperplanes to project the approximate solution vector at each step the algorithm is quasi optimal since the hyperplanes which are determined by the row vectors of the coefficient matrix are selected a priori this is shown to significantly reduce the number of cycles required for convergence we observe that in some cases the ratio of the change vectors of the approximate solution vectors after some number of cycles becomes a constant thus when this occurs a simple geometric acceleration can be applied to calculate the solution directly geometric acceleration can significantly reduce computation time and improve the accuracy of the solution by orders of magnitude the 3 dimensional x projection method was tested against the 2 dimensional x projection method using random and hilbert coefficient matrices and proved superior less c p u time required in nearly every case

von neumann algebras of equivalence relations with nontrivial one cohomology abstract using popa s deformation rigidity theory we investigate prime decompositions of von neumann algebras of the form l r for countable probability measure preserving equivalence relations r we show that l r is prime whenever r is nonamenable ergodic and admits an unbounded 1 cocycle into a mixing orthogonal representation weakly contained in the regular representation this is accomplished by constructing the gaussian extension r of r and subsequently an s malleable deformation of the inclusion l r l r we go on to note a general obstruction to unique prime factorization and avoiding it we prove a unique prime factorization result for products of the form l r 1 l r 2 l r k as a corollary we get a unique factorization result in the equivalence relation setting for products of the form r 1 r 2 r k we finish with an application to the measure equivalence of groups

some oe and w rigidity results for actions by wreath product groups we use deformation rigidity theory in the von neumann algebra framework to study probability measure preserving actions by wreath product groups in particular we single out large families of wreath product groups satisfying various types of orbit equivalence oe rigidity for instance we show that whenever h k are icc property t groups such that h and k admit stably orbit equivalent action and such that h and k are ergodic then automatically is stably orbit equivalent to and h is stably orbit equivalent to k rigidity results for von neumann algebras arising from certain actions of such groups i e w rigidity results are also obtained

the projection method for solving nonlinear systems of equations under the most violated constraint control abstract we extend a block version of kaczmarz s method with the most violated constraint control to the case of a square nonlinear system of equations without convexity assumptions we prove a local linear convergence theorem and show some numerical experiences

ccap for universal discrete quantum groups we show that the discrete duals of the free orthogonal quantum groups have the haagerup property and the completely contractive approximation property analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite dimensional c algebras the proof relies on the monoidal equivalence between free orthogonal quantum groups and su q 2 quantum groups on the construction of a sufficient supply of bounded central functionals for su q 2 quantum groups and on the free product techniques of ricard and xu our results generalize previous work in the kac setting due to brannan on the haagerup property and due to the second author on the ccap

orbit equivalence rigidity and bounded cohomology we establish new results and introduce new methods in the theory of measurable orbit equivalence using bounded cohomology of group representations our rigidity statements hold for a wide uncountable class of groups arising from negative curvature geometry amongst our applications are a measurable mostow type rigidity theorems for products of negatively curved groups b prime factorization results for measure equivalence c superrigidity for orbit equivalence d the first examples of continua of type ii1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic

an lmi approach to stability of systems with severe time delay this note describes the stability problems of uncertain systems with arbitrarily time varying and severe time delay using new lyapunov krasovskii functionals less conservative stability conditions are obtained for such systems the results are illustrated using the numerical examples based on simple linear matrix inequalities

an acceleration scheme for row projection methods abstract cimmino s and kaczmarz s methods are two classes of row projection rp methods for solving structured linear systems efficiently on parallel computers they have been extended for solving nonlinear systems since the convergence rates of the two methods are unsatisfactorily slow several acceleration schemes for the kaczmarz method have been proposed in this paper we refine and improve the existing acceleration techniques and develop a new acceleration scheme for both of the methods the new scheme involves finding points closest to a solution x along some lines since x is not known a priori recursion formulas are derived three new accelerated algorithms two for the linear kaczmarz method and the linear cimmino method and the other one for the nonlinear cimmino method are presented the convergence of the three proposed algorithms is proved the linear accelerated kaczmarz algorithm and cimmino algorithm converge globally the nonlinear accelerated cimmino algorithm converges locally an important characteristic is that the accelerated cimmino method retains the same degree of parallelism as the unaccelerated one results of initial numerical experiments with new algorithms are presented

w superrigidity for bernoulli actions of property t groups we consider group measure space 1 factors m l x arising from bernoulli actions of icc property t groups more generally of groups containing an infinite normal subgroup with the relative property t and prove a rigidity result for homomorphisms m overbar m we deduce that the action x is w superrigid i e if y is any free ergodic measure preserving action such that the factors m l x and m l y are isomorphic then the actions x and y must be conjugate moreover we show that if p m 1 is a projection then pmp does not admit a group measure space decomposition nor a group von neumann algebra decomposition the latter under the additional assumption that is torsion free we also prove a rigidity result for homomorphisms m m this time for in a larger class of groups than above now including products of non amenable groups for certain groups e g f 2 f 2 we deduce that m does not embed into pmp for any projection p m 1 and obtain a description of the endomorphism semigroup of m

on the structural theory of ii1 factors of negatively curved groups ii actions by product groups abstract this paper contains a series of structural results for von neumann algebras arising from measure preserving actions by product groups on probability spaces expanding upon the methods used earlier by the first two authors we obtain new examples of strongly solid factors as well as von neumann algebras with unique or no cartan subalgebra for instance we show that every ii 1 factor associated with a weakly amenable group in the class s of ozawa is strongly solid there is also the following product version of this result any maximal abelian subalgebra of any ii 1 factor associated with a finite product of weakly amenable groups in the class s of ozawa has an amenable normalizing algebra finally pairing some of these results with a cocycle superrigidity result of ioana it follows that compact actions by finite products of lattices in s p n 1 n 2 are virtually w superrigid

parallel and sequential kaczmarz methods for solving underdetermined nonlinear equations abstract we analyze the convergence of iterative process in r n of the type x k 1 x k w k using this theory we prove the local convergence of a sequential kaczmarz type method and a parallel kaczmarz type method for solving underdetermined systems of nonlinear equations some numerical experiences are presented

brief paper robust h filtering for a class of uncertain linear systems with time varying delay this paper deals with the problem of delay dependent robust h filtering for uncertain linear systems with time varying delay two cases of time varying delays are fully considered one is the time varying delay being continuous uniformly bounded while the other is the time varying delay being differentiable uniformly bounded with delay derivative bounded by a constant a stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of h noise attenuation based on a new integral inequality delay dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities lmis through deriving these conditions neither model transformation nor bounding technique for cross terms is employed moreover the relationship between the sufficient conditions for the two cases of time varying delay is disclosed finally two examples are also given to illustrate the effectiveness of the proposed methodology

one cohomology and the uniqueness of the group measure space decomposition of a ii1 factor we provide a unified and self contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a ii1 factor we single out a large class of groups characterized by a one cohomology property and prove that for every free ergodic probability measure preserving action of the associated ii1 factor has a unique group measure space cartan subalgebra up to unitary conjugacy our methods follow closely a recent article of chifan peterson but we replace the usage of peterson s unbounded derivations by thomas sinclair s dilation into a malleable deformation by a one parameter group of automorphisms

l 2 rigidity in von neumann algebras we introduce the notion of l2 rigidity for von neumann algebras a generalization of property t which can be viewed as an analogue for the vanishing of 1 cohomology into the left regular representation of a group we show that l2 rigidity passes to normalizers and is satisfied by nonamenable ii1 factors which are non prime have property or are weakly rigid as a consequence we obtain that if m is a free product of diffuse von neumann algebras or if m l where is a finitely generated group with 1 2 0 then any nonamenable regular subfactor of m is prime and does not have properties or t in particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of n ozawa

robust kalman filtering for continuous time lag systems the linear continuous time kalman filter for a class of time lag systems with norm bounded uncertain parameters is considered we investigate the conditions for linear delayless state estimator such that the estimation error covariance is guaranteed to lie within a prescribed bound for all admissible uncertainties it is proven that a robust kalman filter algorithm can be determined in terms of two riccati equations involving scalar parameters the developed theory is illustrated by numerical simulation

w superrigidity of mixing gaussian actions of rigid groups abstract we generalize w superrigidity results about bernoulli actions of rigid groups to general mixing gaussian actions we thus obtain the following if is any icc group which is w rigid i e it contains an infinite normal subgroup with the relative property t then any mixing gaussian action x is w superrigid more precisely if y is another free ergodic action such that the crossed product von neumann algebras are isomorphic l x l y then the actions are conjugate we prove a similar statement whenever is a non amenable icc product of two infinite groups

filtering continuous time linear systems with time varying measurement delay we consider the filtering problem of lti continuous time systems with known and bounded measurement delays the aim of the technical note is the design of a finite dimensional sub optimal filter whose performance in terms of the estimation error is comparable to optimal infinite dimensional approaches we show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error in the time varying case no restrictive hypotheses on the delay function are needed the proposed filter can therefore be applied to delay functions for which traditional infinite dimensional approaches cannot be straightforwardly applied

strongly solid group factors which are not interpolated free group factors we give examples of non amenable infinite conjugacy classes groups with the haagerup property weakly amenable with constant cb 1 for which we show that the associated ii1 factors l are strongly solid i e the normalizer of any diffuse amenable subalgebra p subset l gamma generates an amenable von neumann algebra nevertheless for these examples of groups l is not isomorphic to any interpolated free group factor l ft for 1 t

w superrigidity for arbitrary actions of central quotients of braid groups for any n geqslant 4 let tilde b n b n z b n be the quotient of the braid group b n through its center we prove that any free ergodic probability measure preserving pmp action tilde b n curvearrowright x mu is virtually hbox w superrigid in the following sense if l infty x rtimes tilde b n cong l infty y rtimes lambda for an arbitrary free ergodic pmp action lambda curvearrowright y nu then the actions tilde b n curvearrowright x lambda curvearrowright y are virtually conjugate moreover we prove that the same holds if tilde b n is replaced with a finite index subgroup of the direct product tilde b n 1 times cdots times tilde b n k for some n 1 ldots n k geqslant 4 the proof uses the dichotomy theorem for normalizers inside crossed products by free groups from popa and vaes 212 141 198 2014 in combination with the oe superrigidity theorem for actions of mapping class groups from kida 131 99 109 2008 similar techniques allow us to prove that if a group gamma is hyperbolic relative to a finite family of proper finitely generated residually finite infinite subgroups then the hbox ii 1 factor l infty x rtimes gamma has a unique cartan subalgebra up to unitary conjugacy for any free ergodic pmp action gamma curvearrowright x mu

non classification of cartan subalgebras for a class of von neumann algebras abstract we study the complexity of the classification problem for cartan subalgebras in von neumann algebras we construct a large family of ii1 factors whose cartan subalgebras up to unitary conjugacy are not classifiable by countable structures providing the first such examples additionally we construct examples of ii1 factors whose cartan subalgebras up to conjugacy by an automorphism are not classifiable by countable structures finally we show directly that the cartan subalgebras of the hyperfinite ii1 factor up to unitary conjugacy are not classifiable by countable structures and deduce that the same holds for any mcduff ii1 factor with at least one cartan subalgebra

a class of ii1 factors with many non conjugate cartan subalgebras abstract we construct a class of ii 1 factors m that admit unclassifiably many cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of m is complete analytic in particular non borel we also construct a ii 1 factor that admits uncountably many non isomorphic group measure space decompositions all involving the same group g so g is a group that admits uncountably many non stably orbit equivalent actions whose crossed product ii 1 factors are all isomorphic

amenable unitary representations of locally compact groups a notion of amenability for an arbitrary unitary group representation is introduced this unifies and generalizes the notions of amenable homogeneous spaces and of inner amenable groups amenable locally compact groups are characterized by the amenability of all their unitary representations amenable representations are characterized by several properties which are operator theoretic analogues of properties characterizing amenable groups we give a generalization to arbitrary representations of hulanicki reiter theorem this is used in order to describe the amenable representations of the groups with kazhdan property t

robust h spl infin filter design for uncertain linear systems with multiple time varying state delays the problem of robust h spl infin filtering for continuous time uncertain linear systems with multiple time varying delays in the state variables is investigated the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain the aim is to design a stable linear filter assuring asymptotic stability and a prescribed h spl infin performance level for the filtering error system irrespective of the uncertainties and the time delays sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities which can be efficiently solved by means of powerful convex programming tools with global convergence assured an example illustrates the proposed methodology

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

unique cartan decomposition for ii1 factors arising from arbitrary actions of free groups we prove that for any free ergodic probability measure preserving action mathbb f n curvearrowright x mu of a free group on n generators mathbb f n 2 leq n leq infty the associated group measure space ii1 factor l infty x rtimes mathbb f n has l x as its unique cartan subalgebra up to unitary conjugacy we deduce that group measure space ii1 factors arising from actions of free groups with different number of generators are never isomorphic we actually prove unique cartan decomposition results for ii1 factors arising from arbitrary actions of a much larger family of groups including all free products of amenable groups and their direct products

a parallel subgradient projections method for the convex feasibility problem abstract an iterative method to solve the convex feasibility problem for a finite family of convex sets is presented the algorithm consists in the application of a generalization of an acceleration procedure introduced by de pierro in a parallel version of the subgradient projections method proposed by censor and lent the generated sequence is shown to converge for any starting point some numerical results are presented

strong rigidity of generalized bernoulli actions and computations of their symmetry groups abstract we study equivalence relations and ii 1 factors associated with quotients of generalized bernoulli actions of kazhdan groups specific families of these actions are entirely classified up to isomorphism of ii 1 factors this yields explicit computations of outer automorphism and fundamental groups in particular every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic ii 1 factors

hnn extensions of von neumann algebras abstract reduced hnn extensions of von neumann algebras as well as c algebras will be introduced and their modular theory factoriality and ultraproducts will be discussed in several concrete settings detailed analysis on them will be also carried out

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

cout des relations d equivalence et des groupes we study a new dynamical invariant for dicrete groups the cost it is a real number in 1 1 n 1 bounded by the number of generators of the group and it is well behaved with respect to finite index subgroups namely the quantities 1 minus the cost are related by multiplying by the index the cost of every infinite amenable group equals 1 we compute it in some other situations including free products free products with amalgamation and hnn extensions over amenable groups and for direct product situations for instance the cost of the free group on n generators equals n we prove that each possible finite value of the cost is achieved by a finitely generated group it is dynamical because it relies on measure preserving free actions on probability borel spaces in most cases groups have fixed price which implies that two freely acting groups which define the same orbit partition must have the same cost it enables us to distinguish the orbit partitions of probability preserving free actions of free groups of different ranks at the end of the paper we give a mercuriale i e a list of costs of different groups the cost is in fact an invariant of ergodic measure preserving equivalence relations and is defined using graphings a treeing is a measurable way to provide every equivalence class orbit with the structure of a simplicial tree this an example of graphing not every relation admits a treeing we prove that every free action of a cost 1 non amenable group is not treeable but we prove that subrelations of treeable relations are treeable we give examples of relations which cannot be produced by an action of any finitely generated group the cost of a relation which can be decomposed as a direct product is shown to be 1 we define the notion for a relation to be a free product or an hnn extension and compute the cost for the resulting relation from the costs of the building blocks the cost is also an invariant of the pairs von neumann algebra cartan subalgebra

a class of ii _1 factors with a unique mcduff decomposition we provide a fairly large class of ii 1 factors n such that m n bar otimes r has a unique mcduff decomposition up to isomorphism where r denotes the hyperfinite ii 1 factor this class includes all ii 1 factors n l infty x rtimes gamma associated to free ergodic probability measure preserving p m p actions gamma curvearrowright x mu such that either a gamma is a free group mathbb f n for some n ge 2 or b gamma is a non inner amenable group and the orbit equivalence relation of the action gamma curvearrowright x mu satisfies a property introduced in jones and schmidt am j math 109 1 91 114 1987 on the other hand settling a problem posed by jones and schmidt in 1985 we give the first examples of countable ergodic p m p equivalence relations which do not satisfy the property of jones and schmidt 1987 we also prove that if mathcal r is a countable strongly ergodic p m p equivalence relation and mathcal t is a hyperfinite ergodic p m p equivalence relation then mathcal r times mathcal t has a unique stable decomposition up to isomorphism finally we provide new characterisations of property gamma for ii 1 factors and of strong ergodicity for countable p m p equivalence relations

technical communique resilient linear filtering of uncertain systems the problem of resilient linear filtering for a class of linear continuous time systems with norm bounded uncertainties is investigated we have considered additive filter gain variations to reflect the imprecision in filter implementation the design problem of resilient linear filter is formulated as a convex optimization problem over linear matrix inequalities as a limiting procedure the case of resilient kalman filter is derived all the developed results are conveniently extended to the case of multiplicative filter gain variations simulation studies are carried out to support the theoretical findings

iterative algorithms for large partitioned linear systems with applications to image reconstruction abstract we present a unifying framework for a wide class of iterative methods in numerical linear algebra in particular the class of algorithms contains kaczmarz s and richardson s methods for the regularized weighted least squares problem with weighted norm the convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for kaczmarz s and richardson s methods the algorithms in the class may be characterized as being group iterative and incorporate relaxation matrices as opposed to a single relaxation parameter we show that some well known iterative methods of image reconstruction fall into the class of algorithms under consideration and are thus covered by the convergence theory we also describe a novel application to truly three dimensional image reconstruction

actions of _ whose ii factors and orbit equivalence relations have prescribed fundamental group we show that given any subgroup f of r which is either countable or belongs to a certain large class of uncountable subgroups there exist continuously many free ergodic measure preserving actions i of the free group with infinitely many generators f1 on probability measure spaces xi i such that their associated group measure space ii1 factors mi l 1 xi o i f1 and orbit equivalence relationsri r f1 y xi have fundamental group equal tof and with mi respectivelyri stably non isomorphic moreover these actions can be taken so thatri has no outer automorphisms and any automorphism of mi is unitary conjugate to an automorphism that acts trivially on the subalgebra l 1 xi of mi

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

rigidity for von neumann algebras given by locally compact groups and their crossed products we prove the first rigidity and classification theorems for crossed product von neumann algebras given by actions of non discrete locally compact groups we prove that for arbitrary free probability measure preserving actions of connected simple lie groups of real rank one the crossed product has a unique cartan subalgebra up to unitary conjugacy we then deduce a w strong rigidity theorem for irreducible actions of products of such groups more generally our results hold for products of locally compact groups that are nonamenable weakly amenable and that belong to ozawa s class mathcal s

classification of type iii bernoulli crossed products abstract crossed products with noncommutative bernoulli actions were introduced by connes as the first examples of full factors of type i i i this article provides a complete classification of the factors p f n f n where f n is the free group and p is an amenable factor with an almost periodic state we show that these factors are completely classified by the rank n of the free group f n and connes s sd invariant we prove similar results for free product groups as well as for classes of generalized bernoulli actions

direct secant updates of matrix factorizations this paper presents a new context for using the sparse broyden update method to solve systems of nonlinear equations the setting for this work is that a newton like algorithm is assumed to be available which incorporates a workable strategy for improving poor initial guesses and providing a satisfactory jacobian matrix approximation whenever required the total cost of obtaining each jacobian matrix or the cost of factoring it to solve for the newton step is assumed to be sufficiently high to make it attractive to keep the same jacobian approximation for several steps this paper suggests the extremely convenient and apparently effective technique of applying the sparse broyden update directly to the matrix factors in the iterations between reevaluations in the hope that fewer fresh factorizations will be required the strategy is shown to be locally and q superlinearly convergent and some encouraging numerical results are presented

solving systems of nonlinear equations by means of an accelerated successive orthogonal projections method abstract in this paper we introduce an acceleration procedure for a block version of the generalization of kaczmarz s method for nonlinear systems of equations we prove a local linear convergence theorem some numerical experiments are presented which show that the new method improves the nonlinear kaczmarz s method without acceleration

an accelerated successive orthogonal projections method for solving large scale linear feasibility problems abstract we consider linear feasibility problems in the standard form ax b 1 x u the successive orthogonal projections method may be used for solving this problem using sparse orthogonal factorizations techniques for computing the projections on ax b we introduce an acceleration technique in order to speed up the generally slow convergence of the method we present some numerical experiments

solution of underdetermined nonlinear equations by stationary iteration methods nonlinear stationary fixed point iterations inr n are considered the perron ostrowski theorem 23 guarantees convergence if the iteration functiong possesses an isolated fixed pointu in this paper a sufficient condition for convergence is given ifg possesses a manifold of fixed points as an application convergence of a nonlinear extension of the method of kaczmarz is proved this method is applicable to underdetermined equations it is appropriate for the numerical treatment of large and possibly ill conditioned problems with a sparse nonsquare jacobian matrix a practical example of this type nonlinear image reconstruction in ultrasound tomography is included

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

new filter design for linear time delay systems abstract this paper develops new robust delay dependent filter design for a class of linear systems with time varying delays and convex bounded parameter uncertainties the design procedure hinges upon the constructive use of an appropriate lyapunov functional plus a free weighting matrices in order to exhibit the delay dependent dynamics the developed approach utilizes smaller number of lmi decision variables thereby leading to less conservative solutions to the delay dependent stability and filtering problems subsequently linear matrix inequalities lmis based conditions are characterized such that the linear delay system is robustly asymptotically stable with an level l 2 gain all the developed results are tested on representative examples

a new design of robust h2 filters for uncertain systems abstract in this paper a structured polynomial parameter dependent approach is proposed for robust h 2 filtering of linear uncertain systems given a stable system with parameter uncertainties residing in a polytope with s vertices the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain a new polynomial parameter dependent idea is introduced to solve the robust h 2 filtering problem which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain or the linearly parameter dependent framework that uses linear convex combinations of s matrices this idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices linear matrix inequality lmi conditions are obtained for the existence of admissible filters and based on these the filter design is cast into a convex optimization problem which can be readily solved via standard numerical software both continuous and discrete time cases are considered the merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods as shown both theoretically and through extensive numerical examples

oe and w superrigidity results for actions by surface braid groups we show that several important normal subgroups of the mapping class group of a surface satisfy the following property any free ergodic probability measure preserving action y x is stablyoe superrigid these include the central quotients of most surface braid groups and most torelli groups and johnson kernels in addition we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice embeddings using these results in combination with previous results from cik13 we deduce that any free ergodic probabilitymeasure preserving action of almost any surface braid group is stablyw superrigid i e it can be completely reconstructed from its vonneumann algebra

row action methods for huge and sparse systems and their applications this paper brings together and discusses theory and applications of methods identified and labelled as row action methods for linear feasibility problems find x in bf r n such that ax leqq b linearly constrained optimization problems minimize f x subject to ax leqq b and some interval convex programming problems minimize f x subject to c leqq ax leqq b the main feature of row action methods is that they are iterative procedures which without making any changes to the original matrix a use the rows of a one row at a time such methods are important and have demonstrated effectiveness for problems with large or huge matrices which do not enjoy any detectable or usable structural pattern apart from a high degree of sparaseness fields of application where row action methods are used in various ways include image reconstruction from projection operations research and game theory learning theory pattern recognition and transportation theory a row action method for the

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

compact actions and uniqueness of the group measure space decomposition of ii1 factors abstract we prove that any ii1 factor l x arising from a compact free ergodic probability measure preserving action of a countable group with positive first l 2 betti number 1 2 0 has a unique group measure space cartan subalgebra up to unitary conjugacy

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

on solid ergodicity for gaussian actions we investigate gaussian actions through the study of their crossed product von neumann algebra the motivational result is chifan and ioana s ergodic decomposition theorem for bernoulli actions chifan and ioana 2010 4 that we generalize to gaussian actions theorem a we also give general structural results theorems 3 4 and 3 8 that allow us to get a more accurate result at the level of von neumann algebras more precisely for a large class of gaussian actions x we show that any subfactor n of l x containing l x is either hyperfinite or is non gamma and prime at the end of the article we show a similar result for bogoliubov actions

strong solidity of free araki woods factors we show that shlyakhtenko s free araki woods factors are strongly solid meaning that for any diffuse amenable von neumann subalgebra that is the range of a normal conditional expectation the normalizer remains amenable this provides the first class of nonamenable strongly solid type iii factors

strong solidity of group factors from lattices in so n 1 and su n 1 abstract we show that the group factors l where is an icc lattice in either so n 1 or su n 1 n 2 are strongly solid in the sense of ozawa and popa 2010 13 this strengthens a result of ozawa and popa 2010 14 showing that these factors do not have cartan subalgebras