unconditional security from noisy quantum storage we consider the implementation of two party cryptographic primitives based on the sole assumption that no large scale reliable quantum storage is available to the cheating party we construct novel protocols for oblivious transfer and bit commitment and prove that realistic noise levels provide security even against the most general attack such unconditional results were previously only known in the so called bounded storage model which is a special case of our setting our protocols can be implemented with present day hardware used for quantum key distribution in particular no quantum storage is required for the honest parties

evolutive information contained in frequency spectra abstract information concerning important details of an ecosystem s evolution are shown to be contained in an appropriately constructed power spectrum in particular it provides an answer to the question of just why power law behavior vanishes in the absence of darwinian competition

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

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

systemes dynamiques non commutatifs et moyennabilite on introduit la notion de fonction de type positif relativement a un systeme dynamique c dont les proprietes sont analogues a celles des fonctions de type positif classiques on montre que dans le cas d un groupe discret g agissant sur une algebre de von neumann m la moyennabilite de l action est equivalente a l existence d une suite bornee de fonctions de type positif sur g a support fini a valeurs dans le centre z m de m qui converge vers 1 pour la topologie de la convergence simple ultrafaible

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

on 1 f noise and other distributions with long tails abstract it is shown following shockley shockley w 1957 proc ire 45 279 290 that when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks the distribution function for successes in the primary task is log normal it is also shown that when the dispersion of the log normal distribution is large the distribution is mimicked by a 1 x distribution over a wide range of x this argument provides a generic set of processes that yields the much observed 1 x distribution and will also lead to a 1 f noise spectrum it is commonly found that distributions that seem to be log normal over a broad range say to the 95th percentile of a population change to an inverse fractional power pareto distribution for the last few percentile annual income distributions are examples with this structure the very wealthy generally achieve their superwealth through amplification processes that are not available to most we have introduced a simple amplification model to characterize the transition from a log normal distribution to an inverse power pareto tail

group c algebras as decreasing intersection of nuclear c algebras we prove that for every exact discrete group gamma there is an intermediate rm c ast algebra between the reduced group rm c ast algebra and the intersection of the group von neumann algebra and the uniform roe algebra which is realized as the intersection of a decreasing sequence of isomorphs of the cuntz algebra cal o 2 in particular when gamma has the ap approximation property the reduced group rm c ast algebra is realized in this way we also study extensions of the reduced free group rm c ast algebras and show that any exact absorbing or unital absorbing extension of it by any stable separable nuclear rm c ast algebra is realized in this way

on c algebras of irreversible algebraic dynamical systems abstract extending the work of cuntz and vershik we develop a general notion of independence for commuting group endomorphisms based on this concept we initiate the study of irreversible algebraic dynamical systems which can be thought of as irreversible analogues of the dynamical systems considered by schmidt to each irreversible algebraic dynamical system we associate a universal c algebra and show that it is a uct kirchberg algebra under natural assumptions moreover we discuss the structure of the core subalgebra which turns out to be closely related to generalized bunce deddens algebras in the sense of orfanos we also construct discrete product systems of hilbert bimodules for irreversible algebraic dynamical systems which allow us to view the associated c algebras as cuntz nica pimsner algebras besides we prove a decomposition theorem for semigroup crossed products of unital c algebras by semidirect products of discrete left cancellative monoids

affine buildings tiling systems and higher rank cuntz krieger algebras to an r dimensional subshift of finite type satisfying certain special properties we associate a c algebra a this algebra is a higher rank version of a cuntz krieger algebra in particular it is simple purely infinite and nuclear we study an example if is a group acting freely on the vertices of an a2 building with finitely many orbits and if is the boundary of that building then c o is the algebra associated to a certain two dimensional subshift

projective repesentations of the hilbert lie group u h 2 via quasifree statres on the car algebra the group u h 2 of unitary operators on a hilbert space h which differ from the identity by a hilbert schmidt operator may be imbedded in the group of bogoliubov automorphisms of the car algebra over h in such a way as to be weakly inner in any gauge invariant quasifree representation consequently each such quasifree representation determines a projective representation of u h 2 if 0 a i is the operator on h determining the quasifree representation a and a denotes the cyclic projective representation of u h 2 generated from the g n s cyclic vector a for a then the 2 cocycle in u h 2 determined by a can be given explicitly we prove that this 2 cocycle is a coboundary if any only if a or 1 a is hilbert schmidt the representations a on restriction to the group u h 1 consisting of unitaries which differ from the identity by a trace class operator always determine 2 cocycles which are coboundaries these representations of u h 1 have already been investigated by stratila and voiculescu lecture notes in mathematics no 486 springer new york 1975 math anal 235 1978 87 110 thus the stratila voiculescu representations of u h 1 always extend to projective representations of u h 2 and to ordinary representations when a or 1 a is hilbert schmidt this fact enables exploitation of the type analysis of stratila and voiculescu to determine the type of the von neumann algebra a u h 2 in the special case where 0 and 1 are not eigenvalues of a a is cyclic and separating for a u h 2 and hence determines a k m s state on this algebra it is shown that for special choices of a type iii 0 1 factors a u h 2 may be constructed

the slice map problem for weakly closed subspaces of von neumann algebras a a weakly closed subspace of b x is said to have propett s if for any a weakly closed subspace 5 of a von neumann algebra i x e 5 0 a r x for all rp e b 0 x l where r is the right slice map associated with t it is shown that semidiscrete von neumann algebras have property sa and various stability properties of the class of a weakly closed subspaces with property s0 are established it is also shown that if 111 g a is a w dynamical system such that k has property s0 and c is compact abelian then all of the spectral subspaces associated with a have property s0 some applications of these results to the study of tensor products of spectral subspaces and tensor products of reflexive algebras are given in particular it is shown that if l is a commutative subspace lattice with totally atomic core and l is an arbitrary subspace lattice then alg i 0 e2 algc1 0 algl 2 introduction slice maps introduced by tomiyama have proved to be a powerful tool in studying tensor products of c algebras and von neumann algebras see e g 23 24 26 281 in this paper we use slice maps to study tensor products of a weakly closed subspaces of von neumann algebras particularly tensor products of spectral subspaces and tensor products of reflexive algebras if t and 6 are von neumann algebras then for each qp in x the predual of x there is a unique a weakly continuous linear map r from 9dz 0 9 to 6 such that r w a x b a q b a e 91r b e dl l called the right slice map associated with p similarly for each 4 e 9l there is a left slice map li from 9dth0 6 to 9dt if 5 c 9th and y c are a weakly closed subspaces and 5 8 5 denotes the a weak closure of the algebraic tensor product of 5 and c it is clear that if x e 0 0 then r x c 9 for all p e 9 x if x e 5 0 r x efor all qg e 5 received by the editors february 19 1982 and in revised form july 20 1982 1980 mathematics subject classification primary 46l10 46l55 46m05 47d25

amenable minimal cantor systems of free groups arising from diagonal actions we study amenable minimal cantor systems of free groups arising from the diagonal actions of the boundary actions and certain cantor systems it is shown that every virtually free group admits continuously many amenable minimal cantor systems whose crossed products are mutually non isomorphic kirchberg algebras in the uct class with explicitly determined k theory the technique developed in our study also enables us to compute the k theory of certain amenable minimal cantor systems we apply it to the diagonal actions of the boundary actions and the products of the odometer transformations and determine their k theory then we classify them in terms of the topological full groups continuous orbit equivalence strong orbit equivalence and the crossed products

optimal phase estimation in quantum networks we address the problem of estimating the phase given n copies of the phase rotation u within an array of quantum operations in finite dimensions we first consider the special case where the array consists of an arbitrary input state followed by any arrangement of the n phase rotations and ending with a povm we optimize the povm for a given input state and fixed arrangement then we also optimize the input state for some specific cost functions in all cases the optimal povm is equivalent to a quantum fourier transform in an appropriate basis examples and applications are given

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

amenability for fell bundles given a fell bundle b over a discrete group we construct its reduced cross sectional algebra c r b in analogy with the reduced crossed products defined for c dynamical systems when the reduced and full cross sectional algebras of b are isomorphic we say that the bundle is amenable we then formulate an approximation property which we prove to be a sufficient condition for amenability a theory of graded c algebras possessing a conditional expectation is developed with an eye on the fell bundle that one naturally associates to the grading we show for instance that all such algebras are isomorphic to c r b when the bundle is amenable we also study induced ideals in graded c algebras and obtain a generalization of results of str til and voiculescu on af algebras and of nica on quasi lattice ordered groups a brief comment is made on the relevance to our theory of a certain open problem in the theory of exact c algebras an application is given to the case of an fn grading of the cuntz krieger algebras oa recently discovered by quigg and raeburn specifically we show that the cuntz krieger bundle satisfies the approximation property and hence is amenable for all matrices a with entries in 0 1 even if a does not satisfy the well known property i studied by cuntz and krieger in their paper

entropy of automorphisms arising from dynamical systems through discrete groups with amenable actions let g aut a be a discrete group which is exact that is admits an amenable action on some compact space then the entropy of an automorphism of the algebra a does not change by the canonical extension to the crossed product a g this is shown for the topological entropy of an exact c algebra a and for the dynamical entropy of an afd von neumann algebra a these have applications to the case of transformations on lebesgue spaces

continuous fields of c algebras coming from group cocycles and actions recently i have been attempting to formulate a suitable c algebraic framework for the subject of deformation quantization 3 19 continuous fields of c algebras provide one of the key elements for this framework the main examples of deformation quantizations which i have constructed up to now in this c algebra framework come from letting either cocycles on groups or actions of groups vary it has thus become necessary to show that one obtains in this way fields of c aigebras that are indeed continuous since this material is of a general nature and can be useful in other situations 4 6 11 13 it has seemed appropriate to give a separate exposition of it in the present article section 1 of this article contains a review of the published results on continuous fields which we will need as well as a discussion of the fact that the approach which we will take involves treating upper and lower semi continuity separately in sect 2 we discuss the continuity of fields of c algebras which arise from varying cocycles on groups while in sect 3 we do the same for actions which vary

the boundary of universal discrete quantum groups exactness and factoriality we study the c algebras and von neumann algebras associated with the universal discrete quantum groups they give rise to full prime factors and simple exact c algebras the main tool in our work is the study of an amenable boundary action yielding the akemann ostrand property finally this boundary can be identified with the martin or the poisson boundary of a quantum random walk

exactness of locally compact groups we give some new characterizations of exactness for locally compact second countable groups in particular we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact hausdorff space this answers an open question by anantharaman delaroche

ghostbusting and property a abstract we show that the roe algebra of a bounded geometry metric space contains non compact ghosts if and only if the space does not have property a

constructions preserving hilbert space uniform embeddability of discrete groups uniform embeddability in a hilbert space introduced by gromov is a geometric property of metric spaces as applied to countable discrete groups it has important consequences for the novikov conjecture exactness introduced and studied extensively by kirchberg and wassermann is a functional analytic property of locally compact groups recently it has become apparent that as properties of countable discrete groups uniform embeddability and exactness are closely related we further develop the parallel between these classes by proving that the class of uniformly embeddable groups shares a number of permanence properties with the class of exact groups in particular we prove that it is closed under direct and free products with and without amalgam inductive limits and certain extensions

busemann points of infinite graphs we provide a geometric condition which determines whether or not every point on the metric boundary of a graph with the standard path metric is a busemann point that is it is the limit point of a geodesic ray we apply this and a related condition to investigate the structure of the metric boundary of cayley graphs we show that groups such as the braid group and the discrete heisenberg group have boundary points of the cayley graph which are not busemann points when equipped with their usual generators

relative nuclearity for c algebras and kk equivalences of amalgamated free products abstract we prove a relative analogue of equivalence between nuclearity and cpap in its proof the notion of weak containment for c correspondences plays an important role as an application we prove kk equivalence between full and reduced amalgamated free products of c algebras under a strengthened variant of relative nuclearity

c operator systems and crossed products abstract the purpose of this paper is to introduce a consistent notion of universal and reduced crossed products by actions and coactions of groups on operator systems and operator spaces in particular we shall put emphasis to reveal the full power of the universal properties of the universal crossed products it turns out to make things consistent one has to perform the constructions in some bigger categories which allow the right framework for studying the universal properties and which are stable under the construction of crossed products even for non discrete groups in the case of operator systems this larger category is what we call a c operator system i e a selfadjoint subspace x of some b h which contains a c algebra a such that a x x x a in the case of operator spaces the larger category is given by what we call c operator bimodules we introduce the notion of crossed products in these categories and show that the classical imai takai and katayama duality theorems for crossed products by group co actions on c algebras extend to our notion of crossed products by c operator systems and c operator bimodules

k theory of certain purely infinite crossed products it was shown by rordam and the second named author that a countable group g admits an action on a compact space such that the crossed product is a kirchberg algebra if and only if g is exact and non amenable this construction allows a certain amount of choice we show that different choices can lead to different algebras at least with the free group

a new look at crossed product correspondences and associated c algebras abstract when a locally compact group acts on a c correspondence it also acts on the associated cuntz pimsner algebra in a natural way hao and ng have shown that when the group is amenable the cuntz pimsner algebra of the crossed product correspondence is isomorphic to the crossed product of the cuntz pimsner algebra in this paper we have a closer look at this isomorphism in the case where the group is not necessarily amenable we also consider what happens at the level of toeplitz algebras

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

minimal ambient nuclear c algebras abstract we provide examples of ambient nuclear c algebras of non nuclear c algebras with no proper intermediate c algebras in particular this gives the first examples of minimal ambient nuclear c algebras of non nuclear c algebras for this purpose we study generic cantor systems of infinite free product groups

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

bimodules in crossed products of von neumann algebras abstract in this paper we study bimodules over a von neumann algebra m in the context of an inclusion m m g where g is a discrete group acting on a factor m by outer automorphisms we characterize the m bimodules x m g that are closed in the bures topology in terms of the subsets of g we show that this characterization also holds for w closed bimodules when g has the approximation property ap a class of groups that includes all amenable and weakly amenable ones as an application we prove a version of mercer s extension theorem for certain w continuous surjective isometric maps on x

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

isoperimetry of group actions the isoperimetric profile of a discrete group was introduced by vershik however it is well defined only for a restrictive class amenable groups we generalize the notion of isoperimetric profile beyond the world of amenable groups by defining isoperimetric profiles of amenable actions of finitely generated groups on compact topological spaces this allows to extend the definition of the isoperimetric profile to all groups which are exact in such a way that for amenable groups it is equal to vershik s isoperimetric profile the main feature of our construction is that it preserves many of the properties known from the classical case we use these results to compute exact asymptotics of the isoperimetric profiles for several classes of non amenable groups

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

the slice map problem and approximation properties we show that a weakly closed subspace j of the bounded operators bh on an infinite dimensional hilbert space h has property s the fubini product lt l for all weakly closed subspaces t b h if and only if j satisfies a certain approximation property which we call the weak approximation property the weak approximation property is implied by but does not imply the weak completely bounded approximation property moreover if j has the weak approximation property then the predual j has the approximation property for banach spaces we also prove analagous results for property s and variations of property s for c algebras as an application of our characterization of subspaces with property s we show that the reflexive algebra tensor product formula alg l1 alg l2 alg l1 l2 is not always valid in fact we show that for each of the types ii1 ii and iii 0 1 there is a separably acting factor m alg l1 of that type and a reflexive algebra a alg l2 such that alg l1 alg l2 is strictly contained in alg l1 l2

small cancellation labellings of some infinite graphs and applications we construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree we use them to define infinite graphical small cancellation presentations of groups this technique allows us to provide examples of groups with exotic properties we construct the first examples of finitely generated coarsely non amenable groups that is groups without guoliang yu s property a that are coarsely embeddable into a hilbert space moreover our groups act properly on cat 0 cubical complexes we construct the first examples of finitely generated groups with expanders embedded isometrically into their cayley graphs in contrast in the case of the gromov monster expanders are not even coarsely embedded we present further applications

measure equivalence rigidity and bi exactness of groups we get three types of results on measurable group theory direct product groups of ozawa s class s groups wreath product groups and amalgamated free products we prove measure equivalence factorization results on direct product groups of ozawa s class s groups as consequences monod shalom type orbit equivalence rigidity theorems follow we prove that if two wreath product groups a g b of non amenable exact direct product groups g with amenable bases a b are measure equivalent then g and are measure equivalent we get bass serre rigidity results on amalgamated free products of non amenable exact direct product groups

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

simple model of evolution with variable system size a simple model of biological extinction with variable system size is presented that exhibits a power law distribution of extinction event sizes the model is a generalization of a model recently introduced by newman proc r soc lond b265 1605 1996 both analytical and numerical analysis show that the exponent of the power law distribution depends only marginally on the growth rate g at which new species enter the system and is equal to the one of the original model in the limit g to infty a critical growth rate g c can be found below which the system dies out under these model assumptions stable ecosystems can only exist if the regrowth of species is sufficiently fast

inner amenable locally compact groups in this paper we study the relationship between amenability inner amenability and property p of a von neumann algebra we give necessary conditions on a locally compact group g to have an inner invariant mean m such that m v 0 for some compact neighborhood v of g invariant under the inner automorphisms we also give a sufficient condition on g satisfied by the free group on two generators or an i c c discrete group with kazhdan s property t e g sl n z n 3 such that each linear form on l 2 g which is invariant under the inner automorphisms is continuous a characterization of inner amenability in terms of a fixed point property for left banach g modules is also obtained

crossed products of the cantor set by free minimal actions of ℤd let d be a positive integer let x be the cantor set and let d act freely and minimally on x we prove that the crossed product c d x has stable rank one real rank zero and cancellation of projections and that the order on k0 c d x is determined by traces we obtain the same conclusion for the c algebras of various kinds of aperiodic tilings

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

public key cryptography based on bounded quantum reference frames we demonstrate that the framework of bounded quantum reference frames has application to building quantum public key cryptographic protocols and proving their security thus the framework we introduce can be seen as a public key analogue of the framework of bartlett et al 1 where a private shared reference frame is shown to have cryptographic application the protocol we present in this paper is an identification scheme which like a digital signature scheme is a type of authentication scheme we prove that our protocol is both reusable and secure under the honest verifier assumption thus we also demonstrate that secure reusable quantum public key authentication is possible to some extent

amenability and exactness for dynamical systems and their c algebras we study the relations between amenability resp amenability at infinity of c dynamical systems and equality or nuclearity resp exactness of the corresponding crossed products

relative property t for the subequivalence relations induced by the action of sl2 z on t2 abstract let s be the equivalence relation induced by the action sl 2 z t 2 2 where 2 denotes the haar measure on the 2 torus t 2 we prove that any ergodic subequivalence relation r of s is either hyperfinite or rigid in the sense of s popa 41 the proof uses an ergodic theoretic criterion for rigidity of countable ergodic probability measure preserving equivalence relations moreover we give a purely ergodic theoretic formulation of rigidity for free ergodic probability measure preserving actions of countable groups

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 ozawa kernels we write explicitly ozawa kernels for group extensions for discrete metric spaces of finite asymptotic dimension of large enough hilbert space compression and for suitable actions of countable groups on metric spaces we also obtain an alternative proof of stability results concerning yu s property a

mean field theory for a simple model of evolution a simple dynamical model for darwinian evolution on its slowest time scale is analyzed its mean field theory is formulated and solved a random neighbor version of the model is simulated as is a one dimensional version in one dimension the dynamics can be described in terms of a repetitious random walker and anomalous diffusion with exponent 0 4 in all cases the model self organizes to a robust critical attractor

exotic crossed products and the baum connes conjecture we study general properties of exotic crossed product functors and characterise those which extend to functors on equivariant c algebra categories based on correspondences we show that every such functor allows the construction of a descent in kk theory and we use this to show that all crossed products by correspondence functors of k amenable groups are kk equivalent we also show that for second countable groups the minimal exact morita compatible crossed product functor used in the new formulation of the baum connes conjecture by baum guentner and willett 4 extends to correspondences when restricted to separable g c algebras it therefore allows a descent in kk theory for separable systems

a new family of representations of virtually free groups we construct a new family of irreducible unitary representations of a finitely generated virtually free group we prove furthermore a general result concerning representations of gromov hyperbolic groups that are weakly contained in the regular representation thus implying that all the representations in this family can be realized on the boundary of as a corollary we obtain an analogue of herz majorization principle