herz schur multipliers of dynamical systems abstract we extend the notion of a herz schur multiplier to the setting of non commutative dynamical systems given a c algebra a a locally compact group g and an action of g on a we define transformations on the reduced crossed product of a by which in the case a c reduce to the classical herz schur multipliers we introduce schur a multipliers establish a characterisation that generalises the classical descriptions of schur multipliers and present a transference theorem in the new setting identifying isometrically the herz schur multipliers of the dynamical system a g with the invariant part of the schur a multipliers we discuss special classes of herz schur multipliers in particular those associated to a locally compact abelian group g and its canonical action on the c algebra c of the dual group

caratheodory toeplitz and nehari problems for matrix valued almost periodic functions in this paper the positive and strictly contractive extension problems for almost periodic matrix functions are treated we present nece ssary and sufficient conditions for the existence of extensions in terms of toeplit z and hankel operators on besicovitch spaces and lebesgue spaces furthermore when a solution exists a special extension the band extension is constructed which enjoys a maximum entropy property a linear fractional parameterization of the set of all extensions is also provided the techniques used xn the proofs include factorizations of matrix valued almost periodic functions and a general algebraic scheme called the band method

approximation properties and approximate identities of ap g for a locally compact group g and 1 p let ap g be the figa talamanca herz algebra then the multiplier algebra ma p g of ap g is a dual space we say that ap g has the approximation property or simply ap in ma p g if there is a net u in ap g such that u 1 in the associated weak topology we prove that ap g has the ap in ma p g if and only if there exists a net a in ap g such that a a a ap g 0 uniformly for a in any compact subset of ap g consequently we have that if ap g has the ap in ma p g then ap g has the approximation property as a banach space in the sense of grothendieck for a discrete group g we also study the relationship between the ap of ap g in ma p g and the weak amenability of g

algebras of almost periodic functions with bohr fourier spectrum in a semigroup hermite property and its applications abstract it is proved that the unital banach algebra of almost periodic functions of several variables with bohr fourier spectrum in a given additive semigroup is an hermite ring the same property holds for the wiener algebra of functions that in addition have absolutely convergent bohr fourier series as applications of the hermite property of these algebras we study factorizations of wiener hopf type of rectangular matrix functions and the toeplitz corona problem in the context of almost periodic functions of several variables

on topological centre problems and sin quantum groups let a be a banach algebra with a faithful multiplication anda a be the quotient banach algebra of a with the left arens product we introduce a natural banach algebra which is a closed subspace of a a but equipped with a distinct multiplication with the help of this banach algebra new characteriza tions of the topological centre zt a a ofa a are obtained and a characterization of zt a a by lau and ulger for a having a bounded approximate identity is extended to all banach algebras the study of this banach algebra motivates us to introduce the notion of sin locally compact quantum groups and the concept of quotient strong arens irregularity we give characterizations of co amenable sin quan tum groups which are even new for locally compact groups our study shows that the sin property is intrinsically related to topological centre problems we also give characterizations of quotient strong arens irregularity for all quantum group algebras within the class of banach algebras introduced recently by the authors we characterize the unital ones generalizing the corresponding result of lau and ulger we study the interrelationships between strong arens irregularity and quotient strong arens irregularity revealing the complex nature of topological centre problems some open questions by lau and ulger on zt a a are also answered

crossed products extensions of lp bounds for amenable actions abstract we will extend earlier transference results due to neuwirth and ricard from the context of noncommutative l p spaces associated with amenable groups to that of noncommutative l p spaces associated with crossed products of amenable actions namely if m g c is a completely bounded fourier multiplier on l p then it extends to the crossed product with similar bounds provided that the action is amenable and trace preserving furthermore our construction also allows to extend g equivariant completely bounded operators acting on the space part to the crossed product provided that the generalized folner sets of the action satisfy certain accretivity property as a corollary we obtain stability results for maximal l p bounds over crossed products we derive using that stability results an application to the boundedness of smooth multipliers in the l p spaces of group algebras

complete metric approximation property for q araki woods algebras abstract by adapting an ultraproduct technique of junge and zeng we prove that radial completely bounded multipliers on q gaussian algebras transfer to q araki woods algebras as a consequence we establish the w complete metric approximation property for all q araki woods algebras we apply the latter result to show that the canonical ultraweakly dense c subalgebras of q araki woods algebras are always qwep

a continuous time observer which converges in finite time it is shown that a continuous time observer which comprises two standard nth order observers and a delay d can observe the state of an nth order linear system in finite time d exactly in particular almost any convergence time d can be assigned independent of the observer eigenvalues

on the operator homology of the fourier algebra and its cb multiplier completion abstract we study various operator homological properties of the fourier algebra a g of a locally compact group g establishing the converse of two results of ruan and xu 35 we show that a g is relatively operator 1 projective if and only if g is in and that a g is relatively operator 1 flat if and only if g is inner amenable we also exhibit the first known class of groups for which a g is not relatively operator c flat for any c 1 as applications of our techniques we establish a hereditary property of inner amenability answer an open question of lau and paterson 24 and answer an open question of anantharaman delaroche 1 on the equivalence of inner amenability and property w in the bimodule setting we show that relative operator 1 biflatness of a g is equivalent to the existence of a contractive approximate indicator for the diagonal g in the fourier stieltjes algebra b g g thereby establishing the converse to a result of aristov runde and spronk 3 we conjecture that relative 1 biflatness of a g is equivalent to the existence of a quasi central bounded approximate identity in l 1 g that is g is qsin and verify the conjecture in many special cases we finish with an application to the operator homology of a c b g giving examples of weakly amenable groups for which a c b g is not operator amenable

solution of the similarity problem for cyclic representations of c algebras in a paper from 1955 13 kadison considered the following problem is any bounded non selfadjoint representation 77 of a c algebra a on a hilbert space h similar to a representation i e does there exist an invertible operator t e b h such that tht t is a representation of a this problem is a natural counterpart to a problem considered by dixmier in 1950 9 is any bounded representation of a group g on a hilbert space similar to a unitary representation the group question was solved in the negative by kunze and stein in 1960 14 which in turn was based on previous work of ehrenpreis and mautner 21 the similarity problem for representations of c algebras is still open although a number of partial results have been obtained using the deep results of connes on infective von neumann algebras 7 and the characterization of nuclear c algebras given in 3 one gets the result fairly easily that every bounded representation of a nuclear c algebra is similar to a representation cf 2 th 3 5 and 5 th 4 1 the similarity problem for bounded cyclic representations of arbitrary c algebras was first considered by barnes in 1 he proved that when 77 is a bounded representation of a c algebra a on a hilbert space h such that 7v a and v a have a common cyclic vector i then there exists a closed infective operator t on h such that t and t are densely defined and such that x tht x t is a representation of a bunce sharpened this in 2 by proving that t can be chosen bounded but not necessarily with bounded inverse he also removed the condition that is cyclic for 7v a finally christensen proved in 5 that every irreducible bounded representation of a c algebra is similar to a representation these two results of bunce and christensen rely on an inequality due to pisier 16 cor 2 3 stating that when s is a bounded linear map from a c algebra a into a c algebra b then for all n e n and a an e a

approximation properties for noncommutative lp spaces associated with lattices in lie groups abstract in 2010 lafforgue and de la salle gave examples of noncommutative l p spaces without the operator space approximation property oap and hence without the completely bounded approximation property cbap to this purpose they introduced the property of completely bounded approximation by schur multipliers on s p denoted ap p cb schur and proved that for p 1 4 3 4 the groups sl n z with n 3 do not have the ap p cb schur since for p 1 the ap p cb schur is weaker than the approximation property of haagerup and kraus ap these groups were also the first examples of exact groups without the ap recently haagerup and the author proved that also the group sp 2 r does not have the ap without using the ap p cb schur in this paper we prove that sp 2 r does not have the ap p cb schur for p 1 12 11 12 it follows that a large class of noncommutative l p spaces does not have the oap or cbap

a new application of random matrices ext c _ mathrm red f_2 is not a group in the process of developing the theory of free probability and free entropy voiculescu introduced in 1991 a random matrix model for a free semicircular system since then random matrices have played a key role in von neumann algebra theory cf v8 v9 the main result of this paper is the following extension of voiculescui s random matrix result let x n 1 x n r be a system of r stochastically independent n i n gaussian self adjoint random matrices as in voiculescui s random matrix paper v4 and let x1 xr be a semi circular system in a c probability space then for every polynomial p in r noncommuting variables lim niaeia p x n 1 o x n r o p x1 xr for almost all o in the underlying probability space we use the result to show that the ext invariant for the reduced c algebra of the free group on 2 generators is not a group but only a semi group this problem has been open since anderson in 1978 found the first example of a c algebra a for which ext a is not a group

the fourier algebra of a measured groupoid and its multipliers abstract the classical definitions of the fourier algebras b g and a g of a locally compact group are extended to an arbitrary measured groupoid g dualities are established between b g and a g and the convolution algebras c g and vn g in the framework of operator modules they are used to generalize results of varopoulos and pisier about littlewood functions and completely bounded multipliers

receding horizon unbiased fir filters for continuous time state space models without a priori initial state information a receding horizon unbiased finite impulse response filter rhuff is proposed for continuous time state space models linearity unbiasedness finite impulse response fir structure and independence of the initial state information will be required in advance in addition to a performance index of minimum variance the proposed rhuff is obtained by directly minimizing the performance index with the unbiasedness constraint the proposed rhuff is represented first in a standard fir form and then in an iterative form it is shown that the rhuff is equivalent to the existing receding horizon rh kalman fir filter the former is more systematic and logical while the latter is heuristic due to the handling of infinite covariance of the initial state information

measurable schur multipliers and completely bounded multipliers of the fourier algebras let g be a locally compact group and a g the fourier algebra of g from 17 in 24 herz de ned the space of herz schur multipliers b2 g he claimed that this space coincided with the space he denoted v g in his article 23 but o2ered no proof of this fact the completely bounded multipliers of the fourier algebra mcba g were de ned by de canniere and haagerup in 8 in was shown by bo zejko and fendler 7 that mcba g 1 4 b2 g isometrically unfortunately this result relies on unpublished work of gilbert entitled convolution operators and banach space tensor products i ii and iii but not widely available however there is a proof of the fact that mcba g 1 4 b2 g due to jolissaint 27 which relies on the representation theorem for completely bounded maps applied to the reduced c algebra c r g in this paper we prove an analogue of the fact that mcba g 1 4 b2 g in fact our result obtains that fact in the case that g is a discrete group and improves upon it in the respect that we obtain a complete isometry where both mcba g and b2 g are given natural operator space structures moreover we show that the natural module action of mcba g on the von neumann algebra generated by the left regular representation vn g extends completely isometrically to a normal action of mcba g on all of b l g the space of bounded operators on l g in fact the image of mcba g in the completely bounded normal maps on b l g consists of l1 g bimodule maps and can be characterised as a certain intrinsic invariant part amongst those maps we feel that our approach is interesting in and of itself since it makes systematic use of modern operator space theoretic techniques pioneered by blecher e2ros haagerup paulsen ruan and smith amongst others it thus gives a starting point for obtaining representations of completely bounded multipliers of kac algebras after 29 or of multipliers of locally compact quantum groups after vaes et al see 47 to support our approach in x 3 we describe the space of measurable schur multipliers v1 x for any suitable measure space x we develop the theory of v1 x fully and systematically our main tools for doing this are the results of smith 41 and blecher and smith 5 which characterise the normal completely bounded maps on the space of all bounded operators on a hilbert space which are module maps over a von neumann algebra we make great use of the weak haagerup tensor product of two von neumann algebras which is

generalized notions of amenability ii this paper continues the investigation of the first two authors begun in part i it is shown that approximate amenability and approximate contractibility are the same properties as are uniform approximate amenability and amenability bounded approximate contractibility and bounded approximate amenability are characterized by the existence of suitable operator bounded approximate identities for the diagonal ideal results are given on banach sequence algebras lipschitz algebras and beurling algebras and on the crucial role of approximate identities a new proof is given for a result due to n gronbaek on characterizing of amenability for beurling algebras

the derivation problem for group algebras if g is a locally compact group then for each derivation d from l 1 g into l 1 g there is a bounded measure m g with d a a a for a l 1 g derivation problem of b e johnson

amenability properties of banach algebra valued continuous functions abstract let x be a compact hausdorff space and a a banach algebra we investigate amenability properties of the algebra c x a of all a valued continuous functions we show that c x a has a bounded approximate diagonal if and only if a has a bounded approximate diagonal if a has a compactly central approximate diagonal unbounded then c x a has a compactly approximate diagonal weak amenability of c x a for commutative a is also considered

approximate identities in approximate amenability abstract we answer several open questions in the theory of approximate amenability for banach algebras first we give examples of banach algebras which are boundedly approximately amenable but which do not have bounded approximate identities this answers a question open since the year 2000 when ghahramani and loy founded the notion of approximate amenability we give a nice condition for a c o direct sum of amenable banach algebras to be approximately amenable which gives us a reasonably large and varied class of such examples then we examine our examples in some detail and thereby find answers to other open questions the two notions of bounded approximate amenability and bounded approximate contractibility are not the same the direct sum of two approximately amenable banach algebras does not have to be approximately amenable and a 1 codimensional closed ideal in a boundedly approximately amenable banach algebra need not be approximately amenable

weakly compact homomorphisms we study the structure of weakly compact homomorphisms between banach algebras in particular it is shown that between many pairs of algebras the only weakly compact homomorphisms are those of finite rank

approximate amenability of tensor products of banach algebras abstract examples constructed by the first author and charles read make it clear that many of the hereditary properties of amenability no longer hold for approximate amenability these and earlier results of the authors also show that the presence of a bounded approximate identity often entails positive results here we show that the tensor product of approximately amenable algebras need not be approximately amenable and investigate conditions under which a and b being approximately amenable implies or is implied by a b or a b being approximately amenable once again the role of having a bounded approximate identity comes to the fore our methods also enable us to prove that if a b is amenable then so are a and b a result proved by barry johnson in 1996 under an additional assumption

noncommutative l p spaces without the completely bounded approximation property for any 1 leq p leq infty different from 2 we give examples of non commutative lp spaces without the completely bounded approximation property let f be a non archimedian local field if p 4 or p 4 3 and r geq 3 these examples are the non commutative lp spaces of the von neumann algebra of lattices in sl r f or in sl r r for other values of p the examples are the non commutative lp spaces of the von neumann algebra of lattices in sl r f for r large enough depending on p we also prove that if r geq 3 lattices in sl r f or sl r r do not have the approximation property of haagerup and kraus this provides examples of exact c algebras without the operator space approximation property

invertibility of toeplitz operators and corona conditions in a strip abstract a toeplitz operator with symbol g such that det g 1 is invertible if there is a non trivial solution to a riemann hilbert problem g with and satisfying the corona conditions in c and c respectively however determining such a solution and verifying that the corona conditions are satisfied are in general difficult problems in this paper on one hand we establish conditions on which are equivalent to the corona conditions but easier to verify if g 1 are analytic and bounded in a strip this happens in particular with almost periodic symbols on the other hand we identify new classes of symbols g for which a non trivial solution to g can be explicitly determined and the corona conditions can be verified by the above mentioned approach thus obtaining invertibility criteria for the associated toeplitz operators

quantum channels arising from abstract harmonic analysis we present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups g beginning with a representation of the measure algebra m g we unify and elaborate on recent counter examples to a conjecture on the structure of fixed point subalgebras in infinite dimensions as well as present an application to the noiseless subsystems method of quantum error correction using a representation of the completely bounded fourier multiplier algebra mcba g we provide a new class of counter examples to the recently solved asymptotic quantum birkhoff conjecture along with a systematic method of producing the examples using a geometric representation of schur maps further properties of our channels including duality quantum capacity and entanglement preservation are discussed along with potential applications to additivity conjectures

on p approximation properties for p operator spaces abstract this paper has a two fold purpose let 1 p we first introduce the p operator space injective tensor product and study various properties related to this tensor product including the p operator space approximation property for p operator spaces on l p spaces we then apply these properties to the study of the pseudofunction algebra pf p g the pseudomeasure algebra pm p g and the figa talamanca herz algebra a p g of a locally compact group g we show that if g is a discrete group then most of approximation properties for the reduced group c algebra c g the group von neumann algebra vn g and the fourier algebra a g related to amenability weak amenability and approximation property of g have the natural p analogues for pf p g pm p g and a p g respectively the p completely bounded multiplier algebra m cb a p g plays an important role in this work

on the connection between sets of operator synthesis and sets of spectral synthesis for locally compact groups we extend the results by froelich and spronk and turowska on the connection between operator synthesis and spectral synthesis for a g to second countable locally compact groups g this gives us another proof that one point subset of g is a set of spectral synthesis and that any closed subgroup is a set of local spectral synthesis furthermore we show that non triangular sets are strong operator ditkin sets and we establish a connection between operator ditkin sets and ditkin sets these results are applied to prove that any closed subgroup of g is a local ditkin set

approximate amenability is not bounded approximate amenability abstract we obtain a new criterion sufficient for approximate amenability of banach algebras and an associated criterion sufficient for approximate amenability of c 0 direct sums of approximately amenable banach algebras we use these criteria to give examples of banach algebras which are approximately amenable but not boundedly approximately amenable thus we answer a question which was open since the year 2004 this is so to speak the complementary result to one of our earlier ones in the paper f ghahramani c j read approximate identities in approximate amenability j funct anal 262 9 2012 3929 3945 where we gave examples of boundedly approximately amenable banach algebras that are not boundedly approximately contractible

amplification of completely bounded operators and tomiyama s slice maps abstract let m n be a pair of von neumann algebras or of dual operator spaces with at least one of them having property s and let be an arbitrary completely bounded mapping on m we present an explicit construction of an amplification of to a completely bounded mapping on m n our approach is based on the concept of slice maps as introduced by tomiyama and makes use of the description of the predual of m n given by effros and ruan in terms of the operator space projective tensor product cf effros and ruan internat j math 1 2 1990 163 j operator theory 27 1992 179 we further discuss several properties of an amplification in connection with the investigations made in may et al arch math basel 53 3 1989 283 where the special case m b h and n b k has been considered for hilbert spaces h and k we will then mainly focus on various applications such as a remarkable purely algebraic characterization of w continuity using amplifications as well as a generalization of the so called ge kadison lemma in connection with the uniqueness problem of amplifications finally our study will enable us to show that the essential assertion of the main result in may et al 1989 concerning completely bounded bimodule homomorphisms actually relies on a basic property of tomiyama s slice maps

haagerup property for c algebras abstract we define the haagerup property for c algebras a and extend this to a notion of relative haagerup property for the inclusion b a where b is a c subalgebra of a let be a discrete group and a normal subgroup of we show that the inclusion a r a r has the relative haagerup property if and only if the quotient group has the haagerup property in particular the inclusion c r c r has the relative haagerup property if and only if has the haagerup property c r has the haagerup property if and only if has the haagerup property we also characterize the haagerup property for in terms of its fourier algebra a

computing norms of free operators with matrix coefficients let g 1 g 2 g n be the generators of the free group f n and denote by its left regular representation a formula for norms of operators of the form a i g i where a i are complex matrices or operators is derived similarly to the formula of akemann and ostrand for the scalar case this formula can be used to compute norms of arbitrary finitely supported convolution operators on the free group essentially the same technique yields a formula for the norms of sums of matrix valued creation and annihilation operators on full fock space finally some results about the numerical evaluation of the formula are proved

examples of weakly amenable discrete quantum groups abstract we prove that the free orthogonal and free unitary quantum groups f o n and f u n are weakly amenable and that their cowling haagerup constant is equal to 1 this is achieved by estimating the completely bounded norm of the projections on the coefficients of irreducible representations of their compact duals an argument of monoidal equivalence then allows us to extend this result to quantum automorphism groups of finite spaces and even yields some examples of weakly amenable non unimodular discrete quantum groups with the haagerup property

corrigendum to automatic continuity and amenability in the non commutative schwartz space j math anal appl 432 2 2015 954 964

ideals of a g and bimodules over maximal abelian selfadjoint algebras this paper is concerned with weak closed masa bimodules generated by a g invariant subspaces of vn g an annihilator formula is established which is used to characterise the weak closed subspaces of b l2 g which are invariant under both schur multipliers and a canonical action of m g on b l2 g via completely bounded maps we study the special cases of extremal ideals with a given null set and for a large class of groups we establish a link between relative spectral synthesis and relative operator synthesis

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

colp spaces the local structure of non commutative lp spaces abstract developing the theory of col p spaces a variation of the non commutative analogue of l p spaces we provide new tools to investigate the local structure of non commutative l p spaces under mild assumptions on the underlying von neumann algebras non commutative l p spaces with grothendieck s approximation property behave locally like the space of matrices equipped with the p norm of the sequences of their singular values as applications we obtain a basis for non commutative l p spaces associated with hyperfinite von neumann algebras with separable predual von neumann algebras generated by free groups and obtain a basis for separable nuclear c algebras

radial multipliers on reduced free products of operator algebras let ai be a family of unital c algebras respectively of von neumann algebras and n0 c we show that if a hankel matrix related to is trace class then there exists a unique completely bounded map m on the reduced free product of the ai which acts as a radial multiplier hereby we generalize a result of wysoczanski for herz schur multipliers on reduced group c algebras for free products of groups

approximate and pseudo amenability of various classes of banach algebras we continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with r j loy it is shown that every boundedly approximately contractible banach algebra has a bounded approximate identity and that the fourier algebra of the free group on two generators is not operator approximately amenable further examples are obtained of l1 semigroup algebras which are approximately amenable but not amenable using these we show that bounded approximate contractibility need not imply sequential approximate amenability results are also given for segal algebras on locally compact groups and algebras of p pseudo functions on discrete groups

ripple free deadbeat control for sampled data systems in this paper the ripple free deadbeat control problem for sampled data systems is considered this control objective is to settle the error to zero for all time after some finite settling time in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled data systems the necessary and sufficient conditions to solve this problem are derived and related to the system type and a method of constructing the ripple free deadbeat control system is presented

a bozejko picardello type inequality for finite dimensional cat 0 cube complexes abstract we prove a bozejko picardello type inequality for finite dimensional cat 0 cube complexes and as a consequence we obtain that a group acting properly on a finite dimensional cat 0 cube complex is weakly amenable with the cowling haagerup constant 1

a family of singular oscillatory integral operators and failure of weak amenability a locally compact group g is said to be weakly amenable if the fourier algebra a g admits completely bounded approximative units new results concerning the family of semidirect products gn sl 2 r hn n 2 together with previously known results are used to settle the question of weak amenability for all real algebraic groups the groups gn fail to be weakly amenable to show this one follows an idea of haagerup for the case n 1 and one is led to the estimation of certain singular radon transforms with product type singularities by representation theory matters are reduced to a problem of obtaining rather nontrivial l bounds for a family of singular oscillatory integral operators in the plane with product type singularities and polynomial phases 1 weak amenability and g let g be a locally compact hausdorff topological group equipped with a left invariant haar measure written dx or dy in integrals we write l g for the usual lebesgue space of equivalence classes of functions on g in this section the symbol will denote the left regular representation of g on l g and f g will denote the convolution of functions f and g on g 1 1 the fourier algebra and pointwise multipliers a matrix coefficient of the left regular representation is a function of the form x 7 x h k h xy k y dy where h and k lie in l g the fourier algebra of g denoted by a g is defined to be the banach space of all these that is a g h k h k l g which is actually a linear space equipped with the norm a inf h 2 k 2 h k the infimum is in fact attained see 12 if g is abelian a function in a g is the fourier transform of a function in l where is the dual group of g all functions in a g are continuous and vanish at infinity the fourier algebra forms a commutative banach algebra under pointwise operations with gel fand spectrum g it has a unit the function 1 if and only if g is compact for proofs of these results and for much more information about the fourier algebra see the original article by eymard 12 or the book by pier 29 research for this paper was supported in part by the australian research council and the national science foundation typeset by ams tex 1 the group von neumann algebra vn g is defined to be the set of all bounded linear operators on l g commuting with right translations suppose that f l g we associate to f the left convolution operator f on l g defined by

a continuous time recursive fixed lag smoother converging in finite time in this technical note we propose a new fixed lag smoother that estimates the fixed delayed state for a stochastic continuous time system the estimation error variance of the proposed smoother is minimized under the constraint that the estimated state converges to the real state exactly in finite time after noises or uncertainties disappear for numerical computing the proposed smoother is represented in a recursive form unlike other approaches any additional processes such as batch processing and sampling data through discrete time techniques are not required to achieve the finite time convergence a numerical example is presented to illustrate the finite time convergence of the proposed smoother in comparison with the asymptotic convergence of an optimal smoother

almost periodic operators in let g be a locally compact group a g the fourier algebra of g b g the fourier stieltjes algebra of g and vn g the von neumann algebra generated by the left regular representation a of g then a g is the predual of vn g vn g is a b g module and a g is a closed ideal of b g let ap g t e vn g u 4 ut is a compact operator from a g into vn g the space of almost periodic operators in vn g let c g be the c algebra generated by i x x e g then c g c ap g for a compact g let e be the rank one operator on l2 g that sends h e l2 g to the constant function f h x dx we have the following results 1 there exists a compact group g such that e e ap g c g 2 for a compact lie group g e e ap g x e e c g xt l g has a unique left invariant mean x g is semisimple 3 if g is an extension of a locally compact abelian group by an amenable discrete group then ap g cq5 g 4 let g fr the free group with r generators 1 r oo if t e vn g and u u t is a compact operator from b g into vn g then t e c g

fir filters and recursive forms for discrete time state space models abstract an fir finite impulse response filter and an fir smoother are introduced for discrete time state space models with system noise the fir structure not only guarantees both the bibo stability and the robustness to some parameter changes but also improves the filter divergence problem it is shown in this paper that impulse responses of both the fir filter and the fir smoother are easily obtained from riccati type difference equations especially for time invariant state space models they are also to be time invariant and finally determined by simple equations on a finite interval for the purpose of implementation recursive forms of the fir filter and smoother are derived using each other as adjoint variables improved characteristics of the fir filter in the divergence problem are demonstrated via a simulation

factorization of matrix functions with subgroup supported fourier coefficients abstract it is proved that if a wiener class matrix function on a connected compact abelian group admits a factorization with respect to a connected compact abelian supergroup then it admits a factorization with respect to the original group in particular all factorization indices are characters of the original group an illustrative example is considered

schur and fourier multipliers of an amenable group acting on non commutative l p spaces consider a completely bounded fourier multiplierof a locally compact group g and take 1 p one can associate toa schur multiplier on the schatten classes sp l 2 g as well as a fourier multiplier on l p lg the non commutative l p space of the group von neumann algebra of g we prove that the completely bounded norm of the schur multiplier is not greater than the completely bounded norm of the l p fourier multiplier when g is amenable we show that equality holds extending a result by neuwirth and ricard to non discrete groups for a discrete group g and in the special case when p 6 2 is an even integer we show the following if there exists a map between l p lg and an ultraproduct of l p m sp l 2 g that intertwines the fourier multiplier with the schur multiplier then g must be amenable this is an obstruction to extend the neuwirth ricard result to non amenable groups

isometric isomorphisms between banach algebras related to locally compact groups let g1 g2 be locally compact groups we prove in this paper that if t is an isometric isomorphism from the banach algebra luc g1 the continuous dual of the banach space of left uniformly continuous functions on g1 equipped with arens multiplication onto luc g2 i then t maps m g1 onto m g2 and li g onto l g2 we also prove that any isometric isomorphism from li g second conjugate algebra of l gi onto ll g2 maps l g1 onto l g2 0 introduction and preliminaries let g1 g2 be locally compact groups let m gi i 1 2 be the banach algebra of regular borel measures on gi a well known result of b e johnson 10 asserts that if t is an isometric isomorphism from m g1 onto m g2 then t maps ll g onto l g2 and hence g1 and g2 must be isomorphic by wendel s theorem 21 in this paper we prove theorem 3 1 c among other things that if t is an isometric isomorphism from ll g1 onto l1 g2 then t maps l1 g1 onto ll g2 this answers affirmatively a question raised in 4 theorem 3 1 c was proved for abelian locally compact groups by lau and losert in 13 and for compact and discrete groups by ghahramani and lau in 4 let g be a locally compact group let c g denote the space of bounded continuous complex valued functions on g with the sup norm topology and luc g denote the closed subspace of bounded left uniformly continuous functions on g i e all f e c g such that the map x lxf from g into c g is continuous where lxf y f xy x y e g then luc g is a banach algebra with the arens multiplication defined by nm f n m1f n m e luc g f e luc g where mlf x m lxf x e g furthermore m g may be identified with a closed subspace of luc g by the natural embedding u f f f x du x f e luc g u e m g it was received by the editors november 1 1988 1980 mathematics subject classification 1985 revision primary 43a20

automatic continuity and amenability in the non commutative schwartz space abstract we show that all positive functionals as well as all derivations of the non commutative schwartz space are continuous we also prove this space is not boundedly approximately amenable however it is approximately amenable

on nonlinear h_ infty filtering for discrete time stochastic systems with missing measurements in this paper the h infin filtering problem is investigated for a general class of nonlinear discrete time stochastic systems with missing measurements the system under study is not only corrupted by state dependent white noises but also disturbed by exogenous inputs the measurement output contains randomly missing data that is modeled by a bernoulli distributed white sequence with a known conditional probability a filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies h infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero initial condition the existence conditions of the desired filter are described in terms of a second order nonlinear inequality such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the lyapunov functionals as a consequence a linear time invariant filter design problem is discussed for the benefit of practical applications and some simplified conditions are obtained finally two numerical simulation examples are given to illustrate the main results of this paper

groups acting on trees and approximation properties of the fourier algebra let be a tree and g a locally compact group acting on by isometries with respect to the natural metric on we construct the series of representations of g parametrized by the complex unit disc associated canonically with the distance on via the matrix coefficients we apply this series to prove that for any group g acting on a tree in such a way that the stabilizer of a vertex is a compact subgroup of g the fourier algebra a g admits an approximate unit bounded in the multiplier norm on a g for the special case of semihomogeneous trees and the full group aut of isometries of we decompose the constructed representations obtaining finally an analytic continuation of the principal series of aut

approximate amenability of k x abstract we show that if a banach space x is fairly close to a hilbert space then the banach algebra k x of all compact operators on x is approximately amenable we use this to give examples of banach spaces x for which k x is approximately amenable but not amenable thus we answer a question on existence of such spaces open since 2000

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

the corona theorem and the canonical factorization of triangular ap matrix functions effective criteria and explicit formulas abstract using results of the companion paper the authors obtain effective criteria for the existence of canonical factorization for new classes of triangular almost periodic matrix functions of the form formula the important role in the proof of necessity in these criteria is played by a result on the stability of canonical ap factorizability obtained in the present paper by finding corona solutions for a pair of binomial almost periodic functions it is possible to calculate explicitly the factors of a canonical factorization for a class of considered matrix functions with trinomial f

sets of multiplicity and closable multipliers on group algebras we undertake a detailed study of the sets of multiplicity in a second countable locally compact group g and their operator versions we establish a symbolic calculus for normal completely bounded maps from the space b l2 g of bounded linear operators on l2 g into the von neumann algebra vn g of g and use it to show that a closed subset e g is a set of multiplicity if and only if the set e s t g g ts 1 e is a set of operator multiplicity analogous results are established for m1 sets and m0 sets we show that the property of being a set of multiplicity is preserved under various operations including taking direct products and establish an inverse image theorem for such sets we characterise the sets of finite width that are also sets of operator multiplicity and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set we show that if g satisfies a mild approximation condition pointwise multiplication by a given measurable function g c defines a closable multiplier on the reduced c algebra view the mathml source of g if and only if schur multiplication by the function n g g c given by n s t ts 1 is a closable operator when viewed as a densely defined linear map on the space of compact operators on l2 g similar results are obtained for multipliers on vn g

2m weak amenability of group algebras a common fixed point property for semigroups is applied to show that the group algebra l1 g of a locally compact group g is 2m weakly amenable for each integer m 1

completely bounded maps and invariant subspaces we provide a description of certain invariance properties of completely bounded bimodule maps in terms of their symbols if mathbb g is a locally compact quantum group we characterise the completely bounded l infty mathbb g bimodule maps that send c 0 hat mathbb g into l infty hat mathbb g in terms of the properties of the corresponding elements of the normal haagerup tensor product l infty mathbb g otimes sigma mathop mathrm h l infty mathbb g as a consequence we obtain an intrinsic characterisation of the normal completely bounded l infty mathbb g bimodule maps that leave l infty hat mathbb g invariant extending and unifying results formulated in the current literature separately for the commutative and the co commutative cases

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