full factors and co amenable inclusions we show that if m is a full factor and n subset m is a co amenable subfactor with expectation then n is also full this answers a question of popa from 1986 we also generalize a theorem of tomatsu by showing that if m is a full factor and sigma g curvearrowright m is an outer action of a compact group g then sigma is automatically minimal and m g is a full factor which has w spectral gap in m finally in the appendix we give a proof of the fact that several natural notions of co amenability for an inclusion n subset m of von neumann algebras are equivalent thus closing the cycle of implications given in anantharaman delaroche s paper in 1995

a valued semicircular systems abstract to a von neurnann algebra a and a set of linear maps ij a a i j i such that a ij ij i a a b l2 i is normal and completely positive we associate a von neumann algebra a this von neumann algebra is generated by a and an a valued semicircular system xi i i associated to in many cases there is a faithful conditional expectation e a a if a is tracial then under certain assumptions on a also has a trace one can think of the construction a as an analogue of a crossed product construction we show that most known algebras arising in free probability theory can be obtained from the complex field by iterating the construction of a particular interest are free krieger algebras which by analogy with crossed products and ordinary krieger factors are defined to be algebras of the form l 0 1 the cores of free araki woods factors are free krieger algebras we study the free krieger algebras and as a result obtain several non isomorphism results for free araki woods factors as another source of classification results for free araki woods factors we compute the invariant of connes for free products of von neumann algebras this computation generalizes earlier work on computation of t s and sd invariants for free product algebras

l 2 homology for von neumann algebras the aim of this paper is to introduce a notion of l homology in the context of von neumann algebras finding a suitable co homology theory for von neumann algebras has been a dream for several generations see kr71a kr71b jkr72 ss95 and references therein one s hope is to have a powerful invariant to distinguish von neumann algebras unfortunately little positive is known about the kadison ringrose cohomology h b m m except that it vanishes in many cases furthermore there does not seem to be a good connection between the bounded cohomology theory of a group and of the bounded cohomology of its von neumann algebra our interest in developing an l cohomology theory was revived by the introduction of lcohomology invariants in the field of ergodic equivalence relations in the paper of gaboriau gab02 his results in particular imply that l betti numbers 2 i of a discrete group are the same for measure equivalent groups i e for groups that can generate isomorphic ergodic measure preserving equivalence relations parallels between the worlds of von neumann algebras and measurable equivalence relations have been noted for a long time starting with the parallel between the work of murray and von neumann mvn and that of h dye dy thus there is hope that an invariant of a group that survives measure equivalence will survive also von neumann algebra equivalence i e will be an invariant of the von neumann algebra of the group the original motivation for our construction comes from the well understood analogy between the theory of ii1 factors and that of discrete groups based on the theory of correspondences con con94 this analogy has been remarkably efficient to transpose analytic properties such as amenability or property t from the group context to the factor context con80 cj and more recently in the breakthrough work of popa popa con03 we use the theory of correspondences together with the algebraic description of l betti numbers given by luck his definition involves the computation of the algebraic group homology with coefficients in the group von neumann algebra following the guiding idea that the category of bimodules over a von neumann algebra is the analogue of the category of modules over a group we are led to the following algebraic definition of l homology of a von neumann algebra m

mean square stability for discrete bounded linear systems in hilbert space the asymptotic behaviour for infinite dimensional discrete linear systems driven by white noise is considered in this paper both the evolution and convergence of the state correlation operators sequence are analysed mean square stability conditions are investigated including a comparison with the deterministic stability problem the particular case of compact operators is considered in some detail

properties of the probabilistic implications and s implications recently grzegorzewski 2011 introduced two new families of fuzzy implication functions called probabilistic implications and probabilistic s implications they are based on conditional copulas and make a bridge between probability theory and fuzzy logic in his previous articles author gave a motivation to his idea and indicates some interesting connections between new families of multivalued implications and the dependence structure of the underlying environment in this paper the laws of contraposition the law of importation and t conditionality are studied for these families of fuzzy implications furthermore we discuss the intersections of both new families of implications with r implications s n implications and ql operations

mean square stability conditions for discrete stochastic bilinear systems necessary and sufficient conditions for mean square stability are proved for the following class of nonlinear dynamical systems finite dimensional bilinear models evolving in discrete time and driven by random sequences the stochastic environment under consideration is characterized only by independence wide sense stationarity and second order properties thus we do not assume random sequences to be gaussian zero mean or ergodic the probability distributions involved are allowed to be arbitrary and unknown limiting state moments are given in terms of the model parameters and disturbances moments

on the law of importation x wedge y longrightarrow z equiv x longrightarrow y longrightarrow z in fuzzy logic the law of importation given by the equivalence x lambda y rarr z equiv xrarr y rarr z is a tautology in classical logic in a implications defined by turksen et al the above equivalence is taken as an axiom in this paper we investigate the general form of the law of importation j t x y z j x j y z where t is a t norm and j is a fuzzy implication for the three main classes of fuzzy implications i e r s and ql implications and also for the recently proposed yager s classes of fuzzy implications i e f and g implications we give necessary and sufficient conditions under which the law of importation holds for r s f and g implications in the case of ql implications we investigate some specific families of ql implications also we investigate the general form of the law of importation in the more general setting of uninorms and t operators for the above classes of fuzzy implications following this we propose a novel modified scheme of compositional rule of inference cri inferencing called the hierarchical cri which has some advantages over the classical cri following this we give some sufficient conditions on the operators employed under which the inference obtained from the classical cri and the hierarchical cri become identical highlighting the significant role played by the law of importation

compressions of free products of von neumann algebras a reduction formula for compressions of von neumann algebra ii 1 factors arising as free products is proved this shows that the fundamental group is bf r for some such algebras additionally by taking a sort of free product with an unbounded semicircular element continuous one parameter groups of trace scaling automorphisms on ii infty factors are constructed this produces type iii 1 factors with core mathcal m otimes b mathcal h where mathcal m can be a full ii 1 factor without the haagerup approximation property

a semi finite algebra associated to a subfactor planar algebra we canonically associate to any planar algebra two type ii factors m the subfactors constructed previously by the authors in guionnet et al 2010 6 are isomorphic to compressions of m to finite projections we show that each m is isomorphic to an amalgamated free product of type i von neumann algebras with amalgamation over a fixed discrete type i von neumann subalgebra in the finite depth case existing results in the literature imply that m m is the amplification a free group factor on a finite number of generators as an application we show that the factors mj constructed in guionnet et al in press 6 are isomorphic to interpolated free group factors l f rj rj 1 2 2j 1 i where 2 is the index of the planar algebra and i is its global index other applications include computations of laws of jones wenzl projections

approximation properties and absence of cartan subalgebra for free araki woods factors abstract we show that all the free araki woods factors h r u t have the complete metric approximation property using ozawa popa s techniques we then prove that every nonamenable subfactor n h r u t which is the range of a normal conditional expectation has no cartan subalgebra we finally deduce that the type iii1 factors constructed by connes in the 70s can never be isomorphic to any free araki woods factor which answers a question of shlyakhtenko and vaes

lyapunov equation for infinite dimensional discrete bilinear systems abstract mean square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences such a convergence preserving property holds for an infinite dimensional bilinear system if and only if the associate lyapunov equation has a unique strictly positive solution

free products of measured equivalence relations abstract for given countable standard equivalence relations over the same unit space we construct their free product which is a measured groupoid related topics such as measures and 2 cocyles on the free product needed to deal with groupoid von neumann algebras are also discussed

some minimization problems for the free analogue of the fisher information abstract we consider the free non commutative analogue introduced by d voiculescu of the concept of fisher information for random variables we determine the minimal possible value of a a if a is a non commutative random variable subject to the constraint that the distribution of a a is prescribed more generally we obtain the minimal possible value of a ij a ij 1 i j d if a ij 1 i j d is a family of non commutative random variables such that the distribution of a a is prescribed where a is the matrix a ij d i j 1 the d d generalization is obtained from the case d 1 via a result of independent interest concerning the minimal value of a ij a ij 1 i j d when the matrix a a ij d i j 1 and its adjoint have a given joint distribution a version of this result describes the minimal value of b ij 1 i j d when the matrix b b ij d i j 1 is selfadjoint and has a given distribution we then show how the minimization results obtained for lead to maximization results concerning the free entropy also defined by voiculescu

the norm of polynomials in large random and deterministic matrices let bf x n x 1 n ldots x p n be a family of n n independent normalized random matrices from the gaussian unitary ensemble we state sufficient conditions on matrices bf y n y 1 n ldots y q n possibly random but independent of xn for which the operator norm of p bf x n bf y n bf y n converges almost surely for all polynomials p limits are described by operator norms of objects from free probability theory taking advantage of the choice of the matrices yn and of the polynomials p we get for a large class of matrices the no eigenvalues outside a neighborhood of the limiting spectrum phenomena we give examples of diagonal matrices yn for which the convergence holds convergence of the operator norm is shown to hold for block matrices even with rectangular gaussian blocks a situation including non white wishart matrices and some matrices encountered in mimo systems

on the suitability of the bandler kohout subproduct as an inference mechanism fuzzy relational inference fri systems form an important part of approximate reasoning schemes using fuzzy sets the compositional rule of inference cri which was introduced by zadeh has attracted the most attention so far in this paper we show that the fri scheme that is based on the bandler kohout bk subproduct along with a suitable realization of the fuzzy rules possesses all the important properties that are cited in favor of using cri viz equivalent and reasonable conditions for their solvability their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets moreover we show that under certain conditions the equivalence of first infer then aggregate fita and first aggregate then infer fati inference strategies can be shown for the bk subproduct much like in the case of cri finally by addressing the computational complexity that may exist in the bk subproduct we suggest a hierarchical inferencing scheme thus this paper shows that the bk subproduct based fri is as effective and efficient as the cri itself

a new construction of factors of type iii1 abstract we give in this paper a new construction of factors of type iii 1 under certain assumptions we can thanks to a result by popa give a complete classification for this family of factors although these factors are never full we can nevertheless in many cases compute connes invariant we obtain a new example of an uncountable family of pairwise non isomorphic factors of type iii 1 with the same invariant

asymptotic structure of free araki woods factors the purpose of this paper is to investigate the structure of shlyakhtenko s free araki woods factors using the framework of ultraproduct von neumann algebras we first prove that all the free araki woods factors gamma h mathbb r u t prime prime are omega solid in the following sense for every von neumann subalgebra q subset gamma h mathbb r u t prime prime that is the range of a faithful normal conditional expectation and such that the relative commutant q cap m omega is diffuse we have that q is amenable next we prove that the continuous cores of the free araki woods factors gamma h mathbb r u t prime prime associated with mixing orthogonal representations u mathbb r rightarrow mathcal o h mathbb r are omega solid type mathrm ii infty factors finally when the orthogonal representation u mathbb r rightarrow mathcal o h mathbb r is weakly mixing we prove a dichotomy result for all the von neumann subalgebras q subset gamma h mathbb r u t prime prime that are globally invariant under the modular automorphism group sigma t varphi u of the free quasi free state varphi u

on the classification of full factors of type iii we introduce a new invariant s m for type iii factors m with no almost periodic weights we compute this invariant for certain free araki woods factors we show that connes invariant r cannot distinguish all isomorphism classes of free araki woods factors we show that there exists a continuum of mutually non isomorphic free araki woods factors each without almost periodic weights

liapunov equations for time varying linear systems abstract liapunov equations for time varying linear systems in hilbert space are given this generalizes datko s result for semigroups time varying linear stochastic systems are also considered and analogous results are obtained

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