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

applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in banach spaces in this paper we study nonlinear ergodic properties for an amenable semigroup of nonexpansive mappings in a banach space we prove that ifsis an amenable semigroup and s tt t s is a nonexpansive semigroup on a closed convex subsetcin a uniformly convex banach spaceesuch that the setf s of common fixed points of s is nonempty then there exists a nonexpansive retractionpfromcontof s such thatptt ttp pfor eacht sandpx co ttx t s for eachx c in this case there exists a net a of finite averages of s such that for eacht sand for each bounded subsetbofc lim a ttx a x 0 and lim tta x a x 0 uniformly forx b also if the norm ofeis frechet differentiable then for eachx c pxis the unique common fixed point in s s co ttsx t s furthermore if is an asymptotically invariant net of means then for eachx c t x converges weakly topx

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

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

comparison between dpcm and hadamard transform coding in the composite coding of the ntsc color tv signal since differential pulse code modulation dpcm and orthogonal transform coding otc are the most fundamental methods of high efficiency coding bit reduction method it is important to clarify the basic coding characteristics of these methods and the difference between them in order to utilize the bit reduction method effectively this paper theoretically as well as experimentally compares the coding efficiency of a dpcm having a two dimensional predictor with that of a two dimensional hadamard transform coding method htc in the intrafield coding of the ntsc composite signal the comparison evidenced that the distinctive difference in coding characteristics between dpcm and htc depends greatly on the power level of carrier chrominance signals that is it is confirmed theoretically and experimentally that the coding efficiency of the htc is far lower than that of the dpcm in the case of a signal having a high power level carrier chrominance signal such as a color bar signal

weak closedness of subspaces of fourier stieltjes algebras and weak continuity of the restriction map let g be a locally compact group and b g the fourier stieltjes algebra of g we study the problem of how weak8 closedness of some translation invariant subspaces of b g is related to the structure of g moreover we prove that for a closed subgroup h of g the restriction map from b g to b h is weak8 continuous only when h is open in g introduction let g be a locally compact group and let b g be the fourier stieltjes algebra of g as defined by eymard 8 recall that b g is the linear span of all continuous positive definite functions on g and can be identified with the banach space dual of c g the group c algebra of g the space b g with the xlorm as dual of c g is a commutative banach algebra with pointwise multiplication and complex conjugation the fourier algebra a g of g is the closed subalgebra of b g generated by the functions in b g with compact support in particular a g is contained in co g the algebra of complex valued continuous functions on g vanishing at infinity as is well known a g is weak dense in b g if and only if g is amenable in 3 translation invariant subalgebras a of b g were studied and it was shown that if such a is weak closed and point separating then it must contain a g however apart from this very little seems to be known about weak closed subspaces of b g the first purpose of this paper is to investigate the relation between weak closedness of certain interesting norm closed translation invariant subspaces of b g and the structure of g secondly we solve the problem of whexl for a closed subgroup h of g the restriction map from b g to b h is weak continuous a brief outline of the paper is as follows in section 2 we estsablish for almost connected locally compact groups g the relation between weclk closed ness of bo g b g n co g in e3 g and the structure of g theorem 2 10 the key result is that for a connected lie group g bo g is weak closed in b g if and only if g is a reductive lie group with compact centre and kazhdan s property t received by the editors december 1s 1995 199l mathematics subject classification primary 22d10 43a30 work supported by nato collaborative research grant crg 940184 g 1997 american mathematical society

ergodic retractions for amenable semigroups in banach spaces with normal structure abstract in this paper we discuss the existence of nonexpansive retraction onto the set of common fixed points assume that t s s s is an amenable semigroup of nonexpansive mappings on a closed convex subset c in a reflexive banach space e such that the set f of common fixed points of is nonempty among other things it is shown that if either c has normal structure or the t s s are affine then there exists a nonexpansive retraction p from c onto f such that p t t t t p p for each t s and every closed convex invariant subset of c is also p invariant in the case that the mappings are affine p is also affine and p x c o t t x t s for each x c and it is unique regarding the latter property our results extend corresponding results of t suzuki some remarks on the set of common fixed points of one parameter semigroups of nonexpansive mappings in banach spaces with the opial property nonlinear anal 58 2004 441 458 and r e bruck a common fixed point theorem for a commuting family of nonexpansive mappings pacific j math 53 1974 59 71

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

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

encoding and progressive transmission of still pictures in ntsc composite format using transform domain methods coding schemes suitable for progressive transmission of still pictures in ntsc composite format are studied transform coding methods based on the discrete cosine transform dct and the walshhadamard transform wht are used the transform coefficients are segmented into groups having similar properties variable blocklength to variable length codes are used to encode the quantized coefficients for each of the groups progressive transmission is achieved by sending the coefficients belonging to particular groups in successive passes over the image results are presented for coding the ntsc signal sampled at four times the color subcarrier frequency with an orthogonal structure and at twice the subcarrier frequency with a hexagonal structure

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

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

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

existence of ergodic retractions for semigroups in banach spaces abstract in this work we prove among other results that if s is a right amenable semigroup and t s s s is a quasi nonexpansive semigroup on a closed convex subset c in a strictly convex reflexive banach space e such that the set f of common fixed points of is nonempty then there exists a quasi nonexpansive retraction p from c onto f such that p t t t t p p for each t s and every closed convex invariant subset of c is also p invariant moreover if the mappings are also affine then t g rode an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space j math anal appl 85 1982 172 178 12 is a quasi contractive affine retraction from c onto f such that t t t t t t t for each t s and t x c o t t x t s for each x c and if r is an arbitrary retraction from c onto f such that r x c o t t x t s for each x c then r t it is shown that if the t t s are f quasi contractive then the results hold without the strict convexity condition on e

an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space abstract j b baillon c r acad sci paris ser a 280 1975 1511 1514 proved an ergodic theorem for a single nonexpansive mapping in a hilbert space which is a nonlinear version of von neumann s mean ergodic theorem in this paper we study the ergodic behavior of a semigroup of nonexpansive mappings we try to find a sequence of means on the semigroup generalizing the cesaro means on n such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed points our method of proof is an appropriate modification of a pazy s proof israel j math 26 1977 197 204 of baillon s theorem

lebesgue type decomposition of subspaces of fourier stieltjes algebras let g be a locally compact group and let a g and b g be the fourier algebra and the fourier stieltjes algebra of g respectively for any unitary representation of g let b g denote the w closed linear subspace of b g generated by all coefficient functions of and b 0 g the closure of b g a c g where a c g consists of all functions in a g with compact support in this paper we present descriptions of b 0 g and its orthogonal complement b s g in b g generalizing a recent result of t miao we show that for some classes of locally compact groups g there is a dichotomy in the sense that for arbitrary either b 0 g 0 or b 0 g a g we also characterize functions in b 0 g a c g b 0 g and study the question of whether b 0 g a g implies that weakly contains the regular representation

reversible decorrelation method for progressive transmission of 3 d medical image in this paper the authors present a new reversible decorrelation method of three dimensional 3 d medical images for progressive transmission progressive transmission of an image permits gradual improvement of image quality while being displayed when the amount of image data is very large as a 3 d medical image the progressive transmission plays an important role in viewing or browsing the image the data structure presented in this paper takes account of interframe correlation as well as intraframe correlation of the 3 d image this type of data structure has been termed the 3 d hierarchy embedded differential image 3 d hedi as was derived from the earlier hedi structure kim et al 1995 experiments were conducted to verify the performance of 3 d hedi in terms of the decorrelation efficiency as well as the progressive transmission efficiency it is compared with those of conventional hierarchy interpolation hint two dimensional 2 d hedi and differential pulse code modulation dpcm experimental results indicate that 3 d hedi outperforms hint 2 d hedi and dpcm in both decorrelation efficiency as well as the progressive transmission efficiency on 3 d medical images

new convexity and fixed point properties in hardy and lebesgue bochner spaces we show that for the hardy class of functions h1 with domain the ball or polydisc in cn a certain type of uniform convexity property the uniform kadec klee huff property holds with respect to the topology of pointwise convergence on the interior which coincides with both the topology of uniform convergence on compacta and the weak topology on bounded subsets of h1 also we show that if a banach space x has a uniform kadec klee huff property then the lebesgue bochner space lp x 1 p must have a related uniform kadec klee huff property consequently by known results the above spaces have normal structure properties and fixed point properties for non expansive mappings

adaptive dct coding of video signals a coefficient by coefficient adaptive discrete cosine transform dct is investigated the interframe dct has been known to possess an adverse effect in that it generates mosquito and blocking noise by analyzing dct for the intraframe and the interframe video signals a new adaptive intra interframe dct is developed cases without and with the movement compensation are discussed separately through simulations it is shown that a substantial improvement gain 1 0 5 0 db sub p p or 0 2 2 0 db sub p p respectively can be obtained by the new adaptive method the improvement is brought about by the reduction of the blocking noise conventionally generated by the coarse quantization of the higher order interframe dct coefficients by calculating the improvement bound a further possibility is discussed

weak fixed point property of reduced fourier stieltjes algebra and generalization of baggett s theorem abstract in this paper we show that if the reduced fourier stieltjes algebra b g of a second countable locally compact group g has either weak fixed point property or asymptotic center property then g is compact as a result we give affirmative answers to open problems raised by fendler and et al in 2013 we then conclude that a second countable group with a discrete reduced dual must be compact this generalizes a theorem of baggett we also construct a compact scattered hausdorff space for which the dual of the scattered c algebra c lacks weak fixed point property the c algebra c provides a negative answer to a question of randrianantoanina in 2010 in addition we prove a variant of bruck s generalized fixed point theorem for the preduals of von neumann algebras furthermore we give some examples emphasizing that the conditions in bruck s generalized conjecture bgc can not be weakened any more

fixed point set of semigroups of non expansive mappings and amenability abstract in this paper we study the fixed point set of a strongly continuous non expansive semigroup s t t t s of a semi topological semigroup s for which cb s is n extremely left amenable also we study the fixed point set of a strongly continuous semigroup of mappings when s is a semigroup which is a sub semigroup of a locally convex topological vector space with addition some applications to harmonic analysis are also provided

nonexpansive retractions and fixed point properties abstract among other results we prove that if a dual banach space e has the weak fixed point property then e has the weak fixed point property for commuting separable semitopological semigroups of nonexpansive mappings and study the existence of ergodic retractions for right amenable semigroups and commuting families of nonexpansive mappings this answers an open problem of lau and mah 1976 12 for commuting separable semi topological semigroups

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

hypergroups and invariant complemented subspaces abstract let k be a hypergroup with a haar measure the purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of l k and c 0 k the class of left translation invariant w subalgebras of l k and finally the class of non zero left translation invariant c subalgebras of c 0 k in the hypergroup context with the goal of finding some relations between these function spaces among other results we construct two correspondences one between closed weil subhypergroups and certain left translation invariant w subalgebras of l k and another between compact subhypergroups and a specific subclass of the class of left translation invariant c subalgebras of c 0 k by the help of these two characterizations we extract some results about invariant complemented subspaces of l k and c 0 k

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

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

logarithmic hodge witt sheaves on normal crossing varieties in this paper we define two kinds homological and cohomological of etale logarithmic hodge witt sheaves on normal crossing varieties over a perfect field of positive characteristic and discuss some fundamental properties in particular puity and duality

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

scene adaptive coder an efficient single pass adaptive bandwidth compression technique using the discrete cosine transform is described the coding process involves a simple thresholding and normalization operation on the transform coefficients adaptivity is achieved by using a rate buffer for channel rate equalization the buffer status and input rate are monitored to generate a feedback normalization factor excellent results are demonstrated for coding of color images at 0 4 bits pixel corresponding to real time color television transmission over a 1 5 mbit s channel

progressive image transmission using vector quantization on images in pyramid form a progressive image transmission scheme in which vector quantization is applied to images represented by pyramids is proposed a mean pyramid representation of an image is first built up by forming a sequence of reduced size images by averaging over blocks of 2 2 pixels a difference pyramid is then built up by taking the differences between successive levels in the mean pyramid progressive transmission is achieved by sending all the nodes in the difference pyramid starting from the top level and ending at the bottom level the kth approximate image can be formed by adding the information of level k to the previously reproduced k 1 st approximation to gain efficiency vector quantization is applied to the difference pyramid of the image on a level by level basis if the errors due to quantization at level k are properly delivered and included in the next level k 1 then it is demonstrated that the original image can be reconstructed an entropy coder is used to encode the final residual error image losslessly thus ensuring perfect reproduction of the original image the experiments demonstrate that it is possible to achieve simultaneously lossless and progressive transmission with compression at the intermediate level the use of vector quantization results in a coding gain over that obtained using only a huffman coder excellent reproduction is achieved at a bit rate of only 0 06 bits pixel

the grothendieck inequality for bilinear forms on c algebras abstract the following generalization of grothendieck s inequality is proved for any bounded bilinear form v on a pair of c algebras a b there exist two states 1 2 on a and two states 1 2 on b such that v x y v 1 x x 2 xx 2 1 2 1 y y 2 yy 2 1 2 for all x a and all y b an inequality of this type was proved a few years ago by pisier in the case where one of the c algebras has the bounded approximation property it follows from the above inequality that any bounded linear map t of a c algebra into the dual of a c algebra has a factorization t r s through a hilbert space such that r s 2 t

progressive refinement using local variance estimators when transmitting an image over a slow communications link it is desired to provide the best display possible in early stages of the transmission progressive refinement attempts to continuously minimize the deviation between the image and its displayed approximation it is shown that this minimization is accomplished by transmitting average values of regions of the image at increasingly fine levels of resolution the optimal refinement strategy is to subdivide the region which maximizes the product of area and pixel variance typically the receiving process cannot determine the pixel variance estimators of the variance can be computed from information already received are developed they are applied to refinement over the spatial distribution of values and simultaneously to refinement over their gray scale quantization the estimators are shown to apply equally well to monochrome and full color image these techniques are implemented with no transmission overhead and are shown to generate qualitatively and quantitatively superior displays

comparative performance of pyramid data structures for progressive image transmission a review of various pyramid data structures for progressive image transmission focusing on the steps involved in forming the pyramid and the performance comparisons is presented the simple mean pyramid its variants including the truncated mean reduced sum difference reduced difference and s transform pyramids and the more general laplacian pyramid are discussed it is also shown that the use of an interpolation function improves the quality of the full resolution approximations both objectively and subjectively

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

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

convergence of a hybrid algorithm for a reversible semigroup of nonlinear operators in banach spaces abstract the purpose of this paper is to study hybrid iterative schemes of halpern types for a semigroup t s s s of relatively nonexpansive mappings on a closed and convex subset c of a banach space with respect to a sequence n of asymptotically left invariant means defined on an appropriate invariant subspace of l s we prove that given a certain sequence n in 0 1 x c we can generate an iterative sequence x n which converges strongly to f x where f x is the generalized projection from c onto the fixed point set f our main result is even new for the case of a hilbert space

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

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

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

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

nonexpansive retractions and nonlinear ergodic theorems in banach spaces on donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d applications non dilatation sans utiliser le concept de moyenne compacte

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

fixed point properties in hardy spaces abstract we prove that the hardy space h 1 on the unit disc of c has the weak fixed point property for left reversible semigroups

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

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

fixed point properties invariant means and invariant projections related to hypergroups abstract let k be a hypergroup with a haar measure this paper consists of two themes fixed point properties for non expansive and affine maps the first theme provides a condition when a non expansive self map on a weak weak compact convex subset of several function spaces over k has a fixed point while the second theme presents some applications of common fixed point properties for affine actions of k

on chow and brauer groups of a product of mumford curves let c1 cd be mumford curves defined over a finite extension of open image in new window and let x c1 cd we shall show the following 1 the cycle map ch0 x n h2d x n d is injective for any non zero integer n 2 the kernel of the canonical map ch0 x hom br x open image in new window defined by the brauer manin pairing coincides with the maximal divisible subgroup in ch0 x

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

fixed points of non expansive mappings associated with invariant means in a banach space in this paper we study the fixed point set of the non expansive mapping t for a banach space with uniformly g teaux differentiable norm when is a multiplicative left invariant mean on l s as an application we establish nonlinear ergodic properties for an extremely amenable semigroup of non expansive mappings in a banach space with uniformly g teaux differentiable norm furthermore we improve a recent result of atsushiba and takahashi s atsushiba w takahashi weak and strong convergence theorems for non expansive semigroups in a banach spaces satisfying opial s condition sci math jpn in press on the fixed point set of non expansive mappings associated with a left invariant mean on a left amenable semigroup

the retractions onto the common fixed points of some families and semigroups of mappings abstract assume that c is a closed convex subset of a reflexive banach space e and t i i i is a family of self mappings on c of type such that f the common fixed point set of is nonempty from our results in this paper it can be derived that a if i i f t i is contained in a 3 dimensional subspace of e then f is a nonexpansive retract of c b if is commutative there exists a retraction r of type from c onto f such that r t i t i r r i and every closed convex invariant subset of c is r invariant the same result holds for a non commutative right amenable semigroup under some additional assumptions moreover the existence of a t i ergodic retraction r of type from c x i l e x i c i i onto f in l e for the family is discussed we also apply some of our results to find ergodic retractions for nonexpansive affine mappings