weak fixed point property and asymptotic centre for the fourier stieltjes algebra of a locally compact group in this paper we show that the fourier stieltjes algebra b g of a non compact locally compact group g cannot have the weak fixed point property for nonexpansive mappings this answers two open problems posed at a conference in marseille luminy in 1989 we also show that a locally compact group is compact exactly if the asymptotic centre of any non empty weak closed bounded convex subset c in b g with respect to a decreasing net of bounded subsets is a non empty norm compact subset in particular when g is compact b g has the weak fixed point property for left reversible semigroups this generalizes a classical result of t c lim for the circle group as a consequence of our main results we obtain that a number of properties some of which were known to hold for compact groups in fact characterize compact groups

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

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

equidistribution in shrinking sets and l 4 norm bounds for automorphic forms we study two closely related problems stemming from the random wave conjecture for maas forms the first problem is bounding the l 4 norm of a maas form in the large eigenvalue limit we complete the work of spinu to show that the l 4 norm of an eisenstein series e z 1 2 it g restricted to compact sets is bounded by sqrt log t g the second problem is quantum unique ergodicity in shrinking sets we show that by averaging over the centre of hyperbolic balls in gamma backslash mathbb h quantum unique ergodicity holds for almost every shrinking ball whose radius is larger than the planck scale this result is conditional on the generalised lindelof hypothesis for hecke maas eigenforms but is unconditional for eisenstein series we also show that equidistribution for hecke maas eigenforms need not hold at or below the planck scale finally we prove similar equidistribution results in shrinking sets for heegner points and closed geodesics associated to ideal classes of quadratic fields

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

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

on moments of twisted l functions we study the average of the product of the central values of two l functions of modular forms f and g twisted by dirichlet characters to a large prime modulus q as our principal tools we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of q and we use the theory of deligne and katz to prove new bounds on bilinear forms in kloosterman sums with power savings when both variables are near the square root of q when at least one of the forms f and g is non cuspidal we obtain an asymptotic formula for the mixed second moment of twisted l functions with a power saving error term in particular when both are non cuspidal this gives a significant improvement on m young s asymptotic evaluation of the fourth moment of dirichlet l functions in the general case the asymptotic formula with a power saving is proved under a conjectural estimate for certain bilinear forms in kloosterman sums

pointwise eventually non expansive action of semi topological semigroups and fixed points abstract in this paper we define pointwise eventually non expansive action of semi topological semigroups and prove fixed point theorems for it as a result we give an affirmative answer without any extra condition on the banach space to an open problem raised by kirk and xu 2008 7 our results also extend and improve fixed point theorems of lim and lau mah

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 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

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

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

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

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

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

the fixed point property via dual space properties abstract a banach space has the weak fixed point property if its dual space has a weak sequentially compact unit ball and the dual space satisfies the weak uniform kadec klee property and it has the fixed point property if there exists e 0 such that for every infinite subset a of the unit sphere of the dual space a a fails to be 2 e separated in particular e convex banach spaces a class of spaces that includes the uniformly nonsquare spaces have the fixed point property

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

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

symmetry for boundary blow up solutions of elliptic equations in a half space abstract in this paper we consider positive solutions of the following boundary blow up problem in half space p u f u x t u on t where t x x 1 x 2 x n x 1 0 n 2 and the nonlinear function f s satisfies for some a 0 f s 0 in 0 a f s in a under suitable conditions we show that this problem has only one positive solution and it must be a function of x1 only

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

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

the fixed point property in banach spaces with the nus property abstract in this paper we show that the weak nearly uniform smooth banach spaces have the fixed point property for nonexpansive mappings

uniqueness of the solution of a semilinear boundary value problem on considere le probleme aux valeurs limites suivant 2 u f x u 0 x u x 0 x sur pour e 0 il y a un e 0 tel que pour 0 e e ce probleme ait une solution positive unique u dans c 2 c

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

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

trilinear forms and the central values of triple product l functions we give an explicit formula for certain global trilinear forms that appear in jacquet s conjecture in terms of local trilinear forms and the central values of triple product l functions

a mean value of a triple product of l functions luo has proven an optimal upper bound for the l 4 norm of dihedral maass forms of large eigenvalue by bounding a mean value of triple product l functions motivated by this result we study a mean value of l functions having similar shape and obtain for it an asymptotic with power savings our work may be helpful in eventually obtaining an asymptotic for the l 4 norm

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

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

the subconvexity problem for rankin selberg l functions and equidistribution of heegner points ii we prove a general subconvex bound in the level aspect for rankin selberg l functions associated with two primitive holomorphic or maass cusp forms over q we use this bound to establish the equidistribution of incomplete galois orbits of heegner points on shimura curves associated with indefinite quaternion algebras over q

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

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

strongly amenable semigroups and nonlinear fixed point properties abstract a semi topological semigroup is strongly left amenable if there is a compact left ideal group in the spectrum of its luc compactification in this paper we want to study those objects and study some fixed point property related to non expansive mapping and other similar kind of mapping

invariant submeans and semigroups of nonexpansive mappings on banach spaces with normal structure abstract in this paper we study the relation between invariant submean and normal structure in a banach space this is used to give an improvement and different proof of a fixed point theorem of lim also of belluce and kirk for commutative semigroups for left reversible semigroup of nonexpansive mappings on weakly compact convex subsets of a banach space with normal structure

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

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

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