banach algebras on compact right topological groups abstract it is shown how the basic constructs of harmonic analysis such as convolution algebras of measures and functions including fourier stieltjes algebras can be developed for compact hausdorff right topological groups in particular the properties and structure of these new objects are compared with their classical analogues in the topological group case

weak amenability of banach algebras on locally compact groups abstract recent work by various authors has considered the implications of banach algebra amenability for various algebras defined over locally compact groups one of the basic tools being the fact that a continuous homomorphic image of an amenable algebra is again amenable in the present paper we look at the consequences of weak amenability here the homomorphism property fails in general however it remains true for suitable direct summands it is this technique that we make much use of here

some fixed point results on l embedded banach spaces abstract in this paper we prove that w fixed point property and w fixed point property are equivalent concepts for l embedded banach spaces which are duals of m embedded spaces similar results will be obtained with respect to the normal structure these equivalences will be applied to establish new fixed point results for different examples we will also prove the existence of fixed points for both nonexpansive and asymptotically regular mappings defined on subsets of l embedded banach spaces which are sequentially compact for the abstract measure topology we will check that our results do not hold in the case of the weak topology

a renorming in some banach spaces with applications to fixed point theory abstract we consider a banach space x endowed with a linear topology and a family of seminorms r k which satisfy some special conditions we define an equivalent norm on x such that if c is a convex bounded closed subset of x which is relatively sequentially compact then every nonexpansive mapping t c c has a fixed point as a consequence we prove that if g is a separable compact group its fourier stieltjes algebra b g can be renormed to satisfy the fpp in case that g t we recover p k lin s renorming in the sequence space l 1 moreover we give new norms in l 1 with the fpp we find new classes of nonreflexive banach spaces with the fpp and we give a sufficient condition so that a nonreflexive subspace of l 1 can be renormed to have the fpp

spaces of compact operators on a hilbert space with the fixed point property abstract every non reflexive subspace of k h the space of compact operators on a hilbert space h contains an asymptotically isometric copy of c 0 this along with a result of besbes shows that a subspace of k h has the fixed point property if and only if it is reflexive

the fixed point property for some generalized nonexpansive mappings and renormings abstract in 2008 t suzuki 33 defined one of most relevant extensions of the notion of nonexpansivity this notion was extended in 15 defining the so called c mappings in the last years some papers have appeared trying to extend the most important results about existence of fixed points for nonexpansive mappings to this wider class of mappings see for instance 2 5 9 10 15 in this paper we continue this project proving that banach spaces with extended unconditional bases satisfy the fixed point property for c mappings if the unconditional constant of the basis is small enough we also begin a new project on renorming with the fixed point property for c mappings proving that any separable banach space can be renormed to satisfy the fixed point property for c mappings in a stable sense that is the space with the new norm satisfies the fixed point property which in addition is inherited by those isomorphic spaces which are close to it in the sense of the banach mazur distance

sigma finite dual dentability indices abstract a characterization of banach spaces admitting uniformly g teaux smooth norms in terms of finite dual dentability indices is given some applications in the area of weak compactness are discussed we also study locally uniformly rotund dual renormings in connection with countable dual dentability indices

fourier stieltjes algebras and measure algebras on compact right topological groups abstract let g be an admissible compact hausdorff right topological group that is a group with a hausdorff topology such that for each a g the map g g a is continuous and the set of a g such that the map g a g is continuous is dense in g such groups arise in the study of distal flows in this paper we study the fourier stieltjes algebra b g the linear span of the continuous positive definite functions on g we show that b g is isomorphic with the fourier stieltjes algebra of an associated compact topological group this result is then applied to obtain some geometric properties including the weak and weak fixed point properties on b g we also study some related properties on the measure algebra m g

reflexivity is equivalent to the perturbed fixed point property for cascading nonexpansive maps in banach lattices abstract using a theorem of dominguez benavides and the strong james distortion theorems we prove that if a banach space is a banach lattice or has an unconditional basis or is a symmetrically normed ideal of operators on an infinite dimensional hilbert space then it is reflexive if and only if it has an equivalent norm that has the fixed point property for cascading nonexpansive mappings this new class of mappings strictly includes nonexpansive mappings also using a theorem of mil man and mil man we show that for the above classes of banach spaces reflexivity is equivalent to the fixed point property for affine cascading nonexpansive mappings further we show that a cascading nonexpansive mapping on a closed bounded convex set in a banach space always has an approximate fixed point sequence

fixed point properties of semigroups of non expansive mappings abstract in recent years there have been considerable interests in the study of when a closed convex subset k of a banach space has the fixed point property i e whenever t is a non expansive mapping from k into k then k contains a fixed point for t in this paper we shall study fixed point properties of semigroups of non expansive mappings on weakly compact convex subsets of a banach space or more generally a locally convex space by considering the classes of bicyclic semigroups we answer two open questions one posted earlier by the first author in 1976 dalhousie and the other posted by t mitchell in 1984 virginia we also provide a characterization for the existence of a left invariant mean on the space of weakly almost periodic functions on separable semitopological semigroups in terms of fixed point property for non expansive mappings related to another open problem raised by the first author in 1976

renormings and the fixed point property in non commutative l1 spaces abstract let m be a finite von neumann algebra it is known that l 1 m and every non reflexive subspace of l 1 m fail to have the fixed point property for non expansive mappings fpp we prove a new fixed point theorem for this class of mappings in non commutative l 1 m banach spaces which lets us obtain a sufficient condition such that a closed subspace of l 1 m can be renormed to satisfy the fpp as a consequence we deduce that the predual of every atomic finite von neumann algebra can be renormed with the fpp

the fixed point property for mappings admitting a center abstract we introduce a class of nonlinear continuous mappings in banach spaces which allow us to characterize the banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping later on we give an application to the existence of zeroes for certain kinds of accretive operators

there is an equivalent norm on l1 that has the fixed point property abstract let k 8 k 1 8 k for all k n and let be the equivalent norm of l 1 defined by a n sup k n k n k a n for all x a n l 1 we prove that l 1 has the fixed point property for nonexpansive self mappings

fixed point properties and proximinality in banach spaces abstract in this paper we prove the existence of a fixed point for several classes of mappings mappings admitting a center nonexpansive mappings asymptotically nonexpansive mappings defined on the closed convex subsets of a banach space satisfying some proximinality conditions in particular we derive a sufficient condition more general than weak star compactness such that if c is a bounded closed convex subset of l 1 satisfying this condition then every nonexpansive mapping t c c has a fixed point

renorming of l1 and the fixed point property abstract for any k n let p k denote the natural projections on l 1 let be an equivalent norm of l 1 that satisfies all of the following four conditions 1 there are 4 and a positive decreasing sequence n in 0 1 such that for any normalized block basis f n of l 1 and x l 1 with p k 1 x x and x k lim sup n f n x 1 x 2 there are two strictly decreasing sequences k and k with lim k k 0 and lim k k 1 such that for any normalized block basis f n of l 1 and x with i p k x x lim inf n f n x 1 k k 1 x 3 for any k n i p k 1 4 the unit ball of l 1 is l 1 c 0 closed in this article we prove that the space l 1 has the fixed point property for the nonexpansive mapping this improves a previous result of the author

failure of the fpp inside an asymptotically isometric free copy of c0 abstract we produce an equivalent renorming of c 0 which fails to contain an asymptotically isometric copy of c 0 yet all of its infinite dimensional subspaces fail to have the fixed point property for nonexpansive mappings on closed bounded convex subsets

order asymptotically isometric copies of l l1 and c0 in banach function spaces abstract we investigate order asymptotically isometric copies of c 0 l and l 1 in kothe spaces firstly we prove a number of general relations between them and we discuss what happens with such copies while passing to kothe dual spaces or vice versa passing to preduals finally we apply the results to characterize certain classes of kothe spaces as orlicz spaces calderon lozanovski spaces orlicz lorentz spaces and musielak orlicz spaces with such copies

compactness and the fixed point property in l1 abstract in this paper we prove that compactness can be characterized by means of the existence of a fixed point for some classes of mappings defined on convex closed subsets of the space l 1 nominally our result involves nonexpansive mappings uniformly lipschitzian mappings and cascading nonexpansive mappings we also extend the results to some more general classes of banach spaces

weak compactness and fixed point property for affine mappings abstract it is shown that a closed convex bounded subset of a banach space is weakly compact if and only if it has the generic fixed point property for continuous affine mappings the class of continuous affine mappings can be replaced by the class of affine mappings which are uniformly lipschitzian with some constant m 1 in the case of c0 the class of affine mappings which are uniformly lipschitzian with some constant m 6 in the case of quasi reflexive james space j and the class of nonexpansive affine mappings in the case of l embedded spaces

solution of the contractive projection problem in this paper we show that the class of j algebras a class of concrete jordan triple systems is stable under the action of norm one projections this result constitutes a general solution to a problem considered by the authors and others specifically our main result is theorem 2 let p be an arbitrary contractive projection defined on a j algebra m then p m is a jordan triple system in the triple product a b c a b c p f ab c t cb a for a b c e p m and p m has a faithful representation as a j algebra

fixed point property for banach algebras associated to locally compact groups abstract in this paper we investigate when various banach algebras associated to a locally compact group g have the weak or weak fixed point property for left reversible semigroups we proved for example that if g is a separable locally compact group with a compact neighborhood of the identity invariant under inner automorphisms then the fourier stieltjes algebra of g has the weak fixed point property for left reversible semigroups if and only if g is compact this generalizes a classical result of t c lim for the case when g is the circle group t

asymptotically isometric copies ofc0in banach spaces abstract if is an uncountable set then any equivalent renorming of c 0 contains an asymptotically isometric copy of c 0 if y is an infinite dimensional closed subspace of c 0 then y contains an asymptotically isometric copy of c 0 if x and y are two infinite dimensional banach spaces and if x contains an asymptotically isometric copy of c 0 then the injective tensor product of x and y x e y contains a complemented asymptotically isometric copy of c 0 similarly if x contains an asymptotically isometric copy of c 0 then the lebesgue bochner space l p 0 1 x contains a complemented asymptotically isometric copy of c 0

near infinity concentrated norms and the fixed point property for nonexpansive maps on closed bounded convex sets abstract in this paper we define the concept of a near infinity concentrated norm on a banach space x with a boundedly complete schauder basis when is such a norm we prove that x has the fixed point property fpp that is every nonexpansive self mapping defined on a closed bounded convex subset has a fixed point in particular p k lin s norm in l 1 14 and the norm p with p p n and lim n p n 1 introduced in 3 are examples of near infinity concentrated norms when p is equivalent to the l 1 norm it was an open problem as to whether l 1 p had the fpp we prove that the norm p always generates a nonreflexive banach space x r p 1 r p 2 r p 3 satisfying the fpp regardless of whether p is equivalent to the l 1 norm we also obtain some stability results

finite dimensional invariant subspaces for algebras of linear operators and amenable banach algebras abstract we study a finite dimensional invariant subspace property similar to fan s theorem on semigroups for arbitrary banach algebras a in terms of amenability of x a the closed subalgebra of a generated by the set of all maximal elements in a with respect to a character as a consequence we offer some applications to the measure algebra m g and the generalized fourier algebra a p g of a locally compact group g

renormings and fixed point property in non commutative l1 spaces ii affine mappings abstract in this paper we prove that every noncommutative l 1 space associated to a finite von neumann algebra can be renormed to satisfy the fixed point property for nonexpansive affine mappings particular examples are l 1 r where r is the hyperfinite i i 1 factor and the function spaces l 1 0 1 and l 1 for any finite measure space this property does not hold for the usual 1 norm

renormings of c0 and the fixed point property it is unknown whether all renormings of c0 fail the fixed point property fpp or not in this note we give a sufficient condition for a renorming of c0 to fail the fpp which is more general than the previously known ones in fact the condition is satisfied for all renormings of c0 we know it also allows us to show that for some usual renormings of c0 not only the whole space but all its infinite dimensional subspaces fail the fpp

dimensionality reduction of collective motion by principal manifolds abstract while the existence of low dimensional embedding manifolds has been shown in patterns of collective motion the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds this is mainly due to the necessary spectral decomposition step which limits control over the mapping from the original high dimensional space to the embedding space here we propose an alternative approach that demands a two dimensional embedding which topologically summarizes the high dimensional data in this sense our approach is closely related to the construction of one dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints specifically we construct a two dimensional principal manifold directly in the high dimensional space using cubic smoothing splines and define the embedding coordinates in terms of geodesic distances thus the mapping from the high dimensional data to the manifold is defined in terms of local coordinates through representative examples we show that compared to existing nonlinear dimensionality reduction methods the principal manifold retains the original structure even in noisy and sparse datasets the principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing and the resulting two dimensional embedding is compared with that of a well established nonlinear dimensionality reduction method

curvilinear component analysis a self organizing neural network for nonlinear mapping of data sets we present a new strategy called curvilinear component analysis cca for dimensionality reduction and representation of multidimensional data sets the principle of cca is a self organized neural network performing two tasks vector quantization vq of the submanifold in the data set input space and nonlinear projection p of these quantizing vectors toward an output space providing a revealing unfolding of the submanifold after learning the network has the ability to continuously map any new point from one space into another forward mapping of new points in the input space or backward mapping of an arbitrary position in the output space

type and cotype in vector valued nakano sequence spaces abstract given a sequence of banach spaces xn n and a sequence of real numbers pn n in 1 the vector valued nakano sequence spaces l pn xn consist of elements xn n in nxn for which there is a constant 0 such that n xn pn

a fixed point characterization of weak compactness in banach spaces with unconditional schauder basis abstract let x be a banach space with an 1 unconditional schauder basis and without isomorphic copies of l 1 c 0 we obtain an equivalent condition to weak compactness by means of a fixed point theorem namely a closed convex bounded subset c of x is weakly compact if and only if every cascading nonexpansive mapping t c c has a fixed point we particularize our results when c is the closed unit ball of the banach space x obtaining a new characterization of reflexivity note that weak compactness is independent of the underlying equivalent norm and that every banach space with an unconditional schauder basis can be renormed to be 1 unconditional

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

the weil etale topology for number rings there should be a grothendieck topology for an arithmetic scheme x such that the euler characteristic of the cohomology groups of the constant sheaf z with compact support at infinity gives up to sign the leading term of the zeta function of x at s 0 we construct a topology the weil etale topology for the ring of integers in a number field whose cohomology groups hl z determine such an euler characterstic if we restrict to 3

reflexivity and the fixed point property for nonexpansive maps abstract connections between reflexivity and the fixed point property for nonexpansive self mappings of nonempty closed bounded convex subsets of a banach space are investigated in particular it is shown that l 1 for uncountable sets and l cannot even be renormed to have the fixed point property as a consequence if an orlicz space on a finite measure space that is not purely atomic is endowed with the orlicz norm the orlicz space has the fixed point property exactly when it is reflexive

asymptotically non expansive actions of strongly amenable semigroups and fixed points abstract in this paper we deal with some fixed point properties for a semi topological semigroup s acting on a compact convex subset k of a banach space we first focus on the space l m c s of left multiplicatively continuous functions on s and its strong left amenability the existence of a compact left ideal group in the lmc compactification of s we then study the relation between left amenability and strong left amenability of l m c s with a common fixed point property for non expansive and asymptotically non expansive actions of s our results improve a result of t mitchell in 1970 and answer an open problem of a t m lau in 2010 for the class of strongly left amenable semi topological semigroups

a renorming of some nonseparable banach spaces with the fixed point property abstract we prove that for every banach space which can be embedded in c 0 for instance reflexive spaces or more generally spaces with m basis there exists an equivalent renorming which enjoys the weak fixed point property for non expansive mappings as a consequence we solve a longtime open question in metric fixed point theory every reflexive banach can be renormed to satisfy the fixed point property furthermore this norm can be chosen arbitrarily closed to the original norm

fixed point properties for semigroups of nonlinear mappings on unbounded sets abstract a well known result of w ray asserts that if c is an unbounded convex subset of a hilbert space then there is a nonexpansive mapping t c c that has no fixed point in this paper we establish some common fixed point properties for a semitopological semigroup s of nonexpansive mappings acting on a closed convex subset c of a hilbert space assuming that there is a point c c with a bounded orbit and assuming that certain subspace of c b s has a left invariant mean left invariant mean or amenability is an important notion in harmonic analysis of semigroups and groups introduced by von neumann in 1929 28 and formalized by day in 1957 5 in our investigation we use the notion of common attractive points introduced recently by s atsushiba and w takahashi

a fixed point characterization of weakly compact sets in l1 μ spaces abstract let be a finite measure space and consider the lebesgue function space l 1 endowed with its standard norm we obtain a characterization of weak compactness for closed bounded convex subsets of l 1 in terms of the existence of fixed points for certain classes of eventually affine uniformly lipschitzian mappings

on super fixed point property and super weak compactness of convex subsets in banach spaces abstract for a nonempty convex set c of a banach space x a self mapping on c is said to a linear respectively affine isometry if it is the restriction of a linear respectively affine isometry defined on the whole space x by means of super weakly compact set theory established in the recent years in this paper we first show that a nonempty closed bounded convex set of a banach space has super fixed point property for affine or equivalently linear isometries if and only if it is super weakly compact and the super fixed point property and the super weak compactness coincide on every closed bounded convex subset of a banach space under equivalent renorming sense with the application of fabian montesinos zizler s renorming theorem we finally show that every strongly super weakly compact generated banach space can be renormed so that every weakly compact convex set has super fixed point property

fixed point properties for semigroups of nonlinear mappings and amenability abstract in this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a banach space we also study a schauder fixed point property for a semitopological semigroup of continuous mappings on a compact convex subset of a separated locally convex space such semigroups properly include the class of extremely left amenable semitopological semigroups the free commutative semigroup on one generator and the bicyclic semigroup s 1 a b a b 1

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

asymptotically isometric copies of c0 and l1 in bochner spaces abstract let x be a banach space and be a finite measure space it is shown that if 1 p resp 1 p l p x contains asymptotically isometric copies of c 0 resp l 1 if and only if x does

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

new families of nonreflexive banach spaces with the fixed point property abstract in this paper we define the concept of sequentially separating norm and we relate it to the fulfillment of the fixed point property for nonexpansive mappings we develop a technique to construct families of nonreflexive banach spaces with the fixed point property different examples will be exhibited we also study the geometry of the banach spaces that can be renormed with a sequentially separating norm

a generalization of a renorming theorem by lin and a new nonreflexive space with the fixed point property which is nonisomorphic to l1 abstract given 1 p we construct a banach space x p hereditarily asymptotically isometric to l 1 so that for n i m k n it contains an isometric copy of i 1 k 1 m k l p n i 1 and x p contains a subspace isomorphic to c 0 where has cardinality c and use a generalization of a renorming theorem of lin to renorm x p in order to have the fixed point property also we give new renormings with the fpp in some known spaces in particular we prove that c 0 has the fixed point property where x i sup i x i i x i 2 i 0 this gives an example of a space without the fpp whose dual an isomorph of l 1 has the fpp

approximation of fixed points for amenable semigroups of nonexpansive mappings in banach spaces abstract the purpose of this paper is to study iterative schemes of browder and halpern types for a semigroup of nonexpansive mappings on a compact convex subset of a smooth and strictly convex banach space with respect to a sequence of strongly asymptotic invariant means defined on an appropriate space of bounded real valued functions of the semigroup various applications to the additive semigroup of nonnegative real numbers and commuting pairs of nonexpansive mappings are also presented

a fixed point theorem for l1 spaces we prove a fixed point theorem for a family of banach spaces notably for l 1 applications include the optimal answer to the derivation problem for group algebras which originated in the 1960s

weak compactness is not equivalent to the fixed point property in c abstract we show that there exists a non weakly compact closed bounded convex subset w of the banach space of convergent sequences c such that every nonexpansive mapping t w w has a fixed point this answers a question left open in the 2003 and 2004 papers of dowling lennard and turett this is also the first example of a non weakly compact closed bounded convex subset w of a banach space x isomorphic to c 0 for which w has the fixed point property for nonexpansive mappings we also prove that the sets w may be perturbed to a large family of non weakly compact closed bounded convex subsets w q of c with the fixed point property for nonexpansive mappings and we discuss similarities and differences with work of goebel and kuczumow concerning analogous subsets of l 1

direct sums of renormings of l1 and the fixed point property abstract let n be an increasing sequence in 0 1 that converges to 1 and let be the equivalent norm of l 1 defined by a k sup n n n k n a k in this article we show that for any m 1 the space i 1 m l 1 1 is not isometrically isomorphic to any subspace of l 1 and it has the fixed point property

on the structure of the set of equivalent norms on l1 with the fixed point property abstract let a be the set of all equivalent norms on l 1 which satisfy the fpp we prove that a contains rays in fact every renorming in l 1 which verifies condition in theorem 2 1 is the starting point of a closed or open ray composed by equivalent norms on l 1 with the fpp the standard norm 1 or p k lin s norm defined in lin 2008 12 are examples of such norms moreover we study some topological properties of the set a with respect to some equivalent metrics defined on the set of all norms on l 1 equivalent to 1

local rotundity structure of generalized orlicz lorentz sequence spaces abstract we give some criteria for extreme points and strong u points in generalized orlicz lorentz sequence spaces which were introduced in p foralewski h hudzik l szymaszkiewicz on some geometric and topological properties of generalized orlicz lorentz sequence spaces math nachr in press cf g g lorentz an inequality for rearrangements amer math monthly 60 1953 176 179 m nawrocki the mackey topology of some f spaces ph d dissertation adam mickiewicz university poznan 1984 in polish some examples show that in these spaces the notion of the strong u point is essentially stronger than the notion of the extreme point this paper is related to the results from a kaminska extreme points in orlicz lorentz spaces arch math 55 1990 173 180 see remark 1

parameter selection for principal curves principal curves are nonlinear generalizations of the notion of first principal component roughly a principal curve is a parameterized curve in which passes through the middle of a data cloud drawn from some unknown probability distribution depending on the definition a principal curve relies on some unknown parameters number of segments length turn etc which have to be properly chosen to recover the shape of the data without interpolating in this paper we consider the principal curve problem from an empirical risk minimization perspective and address the parameter selection issue using the point of view of model selection via penalization we offer oracle inequalities and implement the proposed approach to recover the hidden structures in both simulated and real life data

finite dimensional invariant subspace property and amenability for a class of banach algebras anthony to ming lau and yong zhangabstract motivated by a result of ky fan in 1965 we establish a charac terization of a left amenable f algebra which includes the group algebra andthe fourier algebra of a locally compact group and quantum group algebras or more generally the predual algebra of a hopf von neumann algebra interms of a nite dimensional invariant subspace property this is done by rstrevealing a xed point property for the semigroup of norm one positive lin ear functionals in the algebra our result answers an open question posted intokyo in 1993 by the rst author see 25 problem 5 we also show that theleft amenability of an ideal in an f algebra may determine the left amenabilityof the algebra

dual fixed point property on spaces of continuous functions under equivalent norms abstract a banach space x is said to have the fixed point property if for every closed convex bounded subset c x and for every t c c nonexpansive there is a fixed point a banach space is said to have the dual fixed point property if its dual space x verifies the fixed point property it is a fact that c 0 k fails the dual fixed point property for every locally compact hausdorff set k in this article we study the fulfilment of the dual fixed point property under equivalent norms we prove that c 0 k can be renormed to have the dual fixed point property if and only if k is a countable set in this case we prove that this renorming can be achieved as close to the standard norm on c 0 k as we like for the banach mazur distance we further obtain the corresponding weak fixed point property stability coefficient regarding the duality c 0 k c 0 k it will be displayed that the value of this stability coefficient strongly depends on the distribution of the accumulation points of k finally we prove that the dual fixed point property is completely unstable for the banach mazur distance in most of nonreflexive banach spaces

orthogonality and disjointness preserving linear maps between fourier and fourier stieltjes algebras of locally compact groups this paper is devoted to the study of orthogonality and disjointness preserving linear maps between fourier and fourier stieltjes algebras of locally compact groups we show that a linear bijection a g1 a g2 resp b g1 b g2 between two fourier algebras resp fourier stieltjes algebras of locally compact groups will induce a topological group isomorphism between g1 and g2 provided that preserves both disjointness and some kind of orthogonality this improves earlier results of j j font and m s monfared where amenability of the groups or continuity of the linear maps are assumed we also study the structure of bounded and unbounded disjointness preserving linear functionals of fourier algebras in the development general results about disjointness and orthogonality preserving linear maps between c algebras w algebras and their preduals are obtained

on banach space properties that are not invariant under the banach mazur distance 1 abstract we consider which properties of banach spaces are not invariant under the banach mazur distance 1 we will say that a given property p is not invariant under the banach mazur distance 1 if there exist two banach spaces x and y such that x has property p y fails property p and the banach mazur distance d x y 1 the main results of this paper concern the case of separable lindenstrauss spaces first in the setting of preduals of l 1 we give some geometric equivalences for polyhedral properties next we show that even in the restricted framework of preduals of l 1 most of the notions of polyhedral banach spaces and their geometric equivalences fail to be invariant under the banach mazur distance 1 then in the general case of banach spaces we indicate some other geometrical properties that are invariant or not invariant under the banach mazur distance 1

distortion and stability of the fixed point property for non expansive mappings abstract let x be a banach space we say that x satisfies the fixed point property weak fixed point property if every non expansive mapping defined from a convex closed bounded convex weakly compact subset of x into itself has a fixed point we say that x satisfies the stable fixed point property stable weak fixed point property if the same is true for every equivalent norm which is close enough to the original one denote by p x the set formed by all equivalent norms with the topology of the uniform convergence on the unit ball of x we prove that the subset of p x formed by the norms failing the fixed point property is dense in p x when x is a non distortable space which fails the fixed point property in particular no renorming of l 1 can satisfy the stable fixed point property furthermore we show some examples of distortable spaces failing the weak fixed point property which can be renormed to satisfy the stable weak fixed point property as a consequence we prove that every separable banach space can be renormed to satisfy the stable weak fixed point property

asymptotically isometric copies of c0 and l1 in certain banach spaces abstract if x is a separable banach space then x contains an asymptotically isometric copy of l1 if and only if there exists a quotient space of x which is asymptotically isometric to c0 if x is an infinite dimensional normed linear space and y is any banach space containing an asymptotically isometric copy of c0 then l x y contains an isometric copy of l if x and y are two infinite dimensional banach spaces and y contains an asymptotically isometric copy of c0 then k w x y contains a complemented asymptotically isometric copy of c0

a simple algorithm for nearest neighbor search in high dimensions the problem of finding the closest point in high dimensional spaces is common in pattern recognition unfortunately the complexity of most existing search algorithms such as k d tree and r tree grows exponentially with dimension making them impractical for dimensionality above 15 in nearly all applications the closest point is of interest only if it lies within a user specified distance spl epsiv we present a simple and practical algorithm to efficiently search for the nearest neighbor within euclidean distance spl epsiv the use of projection search combined with a novel data structure dramatically improves performance in high dimensions a complexity analysis is presented which helps to automatically determine spl epsiv in structured problems a comprehensive set of benchmarks clearly shows the superiority of the proposed algorithm for a variety of structured and unstructured search problems object recognition is demonstrated as an example application the simplicity of the algorithm makes it possible to construct an inexpensive hardware search engine which can be 100 times faster than its software equivalent a c implementation of our algorithm is available

semigroup of nonexpansive mappings on a hilbert space soit s un semi groupe semi topologique soit h un espace de hilbert et s t s s s une representation continue de s comme applications non dilatation sur un sous ensemble convexe clos c de h dans c soit x c on etudie la convergence de t s x s s vers un point fixe commun z de s dans c

fixed point properties of semigroups of nonexpansive mappings abstract we prove that if h is a hilbert space then the schatten trace class operators on h has the weak fixed point property for left reversible semigroups this answered positively a problem raised by a t m lau we also prove that if m is a finite von neumann algebra then any nonempty bounded convex subset of the non commutative l 1 space associated to m that is compact for the measure topology has the fixed point property for left reversible semigroups

some geometric properties on the fourier and fourier stieltjes algebras of locally compact groups arens regularity and related problems let g be a locally compact topological group and a g b g be respectively the fourier and fourier stieltjes algebras of g it is one of the purposes of this paper to investigate the rnp radon nikodym property and some other geometric properties such as weak rnp the dunford pettis property and the schur property on the algebras a g and b g and to relate these properties to the properties of the multiplication operator on the group c algebra c g we also investigate the problem of arens regularity of the projective tensor products c g a when b g c g has the rnp and a is any c algebra some related problems on the measure algebra the group algebra and the algebras a p g pf p g pm p g 1 p are also discussed

fixed point property and the fourier algebra of a locally compact group we establish some characterizations of the weak fixed point property weak fpp for noncommutative and commutative l 1 spaces and use this for the fourier algebra a g of a locally compact group g in particular we show that if g is an in group then a g has the weak fpp if and only if g is compact we also show that if g is any locally compact group then a g has the fixed point property fpp if and only if g is finite furthermore if a nonzero closed ideal of a g has the fpp then g must be discrete

the daugavet property in the musielak orlicz spaces abstract we show that among all musielak orlicz function spaces on a finite non atomic complete measure space equipped with either the luxemburg norm or the orlicz norm the only spaces with the daugavet property are l 1 l l 1 1 l and l 1 l in particular we obtain complete characterizations of the daugavet property in the weighted interpolation spaces the variable exponent lebesgue spaces nakano spaces and the orlicz spaces

normal structure in dual banach spaces associated with a locally compact group in this paper we investigated when the dual of a certain function space defined on a locally compact group has certain geometric properties more particularly we asked when weak compact convex subsets in these spaces have normal structure and when the norm of these spaces satisfies one of several types of kadec klee property as samples of the results we have obtained we have proved among other things the following two results 1 the measure algebra of a locally compact group has weak normal structure iff it has property sukk iff it has property skk iff the group is discrete 2 among amenable locally compact groups the fourier stieltjes algebra has property sukk iff it has property skk iff the group is compact consequently the fourier stieltjes algebra has weak normal structure when the group is compact

banach spaces with a basis that are hereditarily asymptotically isometric to l1 and the fixed point property abstract we show that there is an equivalent norm in a banach space with a basis which is hereditarily asymptotically isometric to l 1 such that every subspace has in turn a subspace with the fixed point property also we give an example of a family of non reflexive spaces not isomorphic to l 1 having the fixed point property and other related examples

fourier stieltjes algebra of a topological group abstract this paper is an invitation to the study of the fourier stieltjes algebra b g the linear span of the continuous positive definite complex valued functions on a topological group g we study b g when g has a host algebra or a group c algebra the analogue of the group c algebra of a locally compact group our main challenge is that a topological group g cannot have a positive regular borel measure which is left translation invariant unless g is locally compact

renormings failing to have asymptotically isometric copies of l1 or c0 abstract it is proved that every equivalent norm in l 1 is the starting point of a ray of norms which fail to have an asymptotically isometric copy of l 1 in the case where x is separable it is proved that the set of all equivalent norms in x which fail to have an asymptotically isometric copy of l 1 is residual similar results are obtained for the case of c 0 in particular we deduce that every separable banach space has an equivalent norm for which it fails to contain an asymptotically isometric copy of l 1 and c 0

asymptotically isometric copies ofc0and renormings of banach spaces abstract if a banach space x contains an asymptotically isometric copy of c 0 then x fails to have weak normal structure consequently if x is an infinite dimensional subspace of c 0 then x fails to have weak normal structure also every equivalent renorming of c 0 for uncountable fails to have weak normal structure every separable banach space can be equivalently renormed so as not to contain an asymptotically isometric copy of c 0 every banach space with the generalized gossez lami dozo ggld property fails to contain a subspace isomorphic to c 0

type and cotype of musielak orlicz sequence spaces let n be a musielak orlicz function and l the musielak orlicz sequence space generated by it is shown that satisfies condition qiff is equivalent to aq concave function n it is also proved thatl is of cotypeq typep if and only if satisfies condition q 2and pconditions respectively as applications we obtain characterization of the type and cotype of various sequence spaces nakano weighted orlicz and orlicz sequence spaces furthermore a relation betweenq concavity p convexity lowerq estimate upperp estimate and cotype type of l is given

hilbert generated spaces we classify several classes of the subspaces of banach spaces x for which there is a bounded linear operator from a hilbert space onto a dense subset in x dually we provide optimal affine homeomorphisms from weak star dual unit balls onto weakly compact sets in hilbert spaces or in c0 spaces in their weak topology the existence of such embeddings is characterized by the existence of certain uniformly g teaux smooth norms

weil etale cohomology of curves over p adic fields abstract recent research has demonstrated a connection between weil etale cohomology and special values of zeta functions in particular lichtenbaum has shown that the order of vanishing and leading coefficient of the zeta function of a smooth projective variety over a finite field has a weil etale cohomological interpretation in terms of certain secondary euler characteristics these results rely on a duality theorem stated in terms of cup product in weil etale cohomology we define weil etale cohomology for varieties over p adic fields and prove a duality theorem for the cohomology of g m on a smooth proper geometrically connected curve of index 1 this duality theorem is a p adic analogue of lichtenbaum s weil etale duality theorem for curves over finite fields as well as a weil etale analogue of his classical duality theorem for curves over p adic fields finally we show that our duality theorem implies this latter classical duality theorem for index 1 curves

amenability and weak amenability of the fourier algebra let g be a locally compact group we show that its fourier algebra a g is amenable if and only if g has an abelian subgroup of finite index and that its fourier stieltjes algebra b g is amenable if and only if g has a compact abelian subgroup of finite index we then show that a g is weakly amenable if the component of the identity of g is abelian and we prove some partial results towards the converse

isometric copies of c0 and l in duals of banach spaces abstract let x be a banach space then x contains an isometric copy of l if and only if x contains an asymptotically isometric copy of c0

lichtenbaum tate duality for varieties over p adic fields s lichtenbaum has proved in l1 that there is a nondegenerate pairing pic c x br c br k q z 1 between the picard group and the brauer group of a nonsingular projective curve c over a p adic field k a finite extension of the p adic numbers qp his proof consists of a reduction via explicit cocycle calculations in galois cohomology to a combination of tate duality for group schemes over p adic fields and the autoduality of the jacobian of a smooth curve in this paper we will reconstruct the above duality as a purely formal combination of a generalized form of tate duality over p adic fields and a form of poincar e duality for curves over arbitrary fields of characteristic zero this gives a more conceptual proof of lichtenbaum s result and an analogue in higher dimensions