Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Stanislaw Prus and Andrzej Wisnicki
by Dale Alspach 21 Jun '07

21 Jun '07

This is an announcement for the paper "On the fixed point property in direct sums of Banach spaces with strictly monotone norms" by Stanislaw Prus and Andrzej Wisnicki. Abstract: It is shown that if a Banach space X has the super fixed point property for nonexpansive mappings or admits a 1-unconditional basis and Y satisfies property asymptotic (P) (which is weaker than the condition WCS(Y)>1), then the direct sum of X and Y endowed with a strictly monotone norm enjoys the weak fixed point property. Archive classification: math.FA Mathematics Subject Classification: 47H09; 46B20 Remarks: 12 pages The source file(s), direct_p.tex: 35126 bytes, is(are) stored in gzipped form as 0706.0915.gz with size 10kb. The corresponding postcript file has gzipped size 86kb. Submitted from: awisnic(a)golem.umcs.lublin.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0915 or http://arXiv.org/abs/0706.0915 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0915 or in gzipped form by using subject line get 0706.0915 to: math(a)arXiv.org.

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Abstract of a paper by Edward Odell, Thomas Schlumprecht and Andras Zsak
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "A new infinite game in Banach spaces with applications" by Edward Odell, Thomas Schlumprecht and Andras Zsak. Abstract: We consider the following two-player game played on a separable, infinite-dimensional Banach space X. Player S chooses a positive integer k_1 and a finite-codimensional subspace X_1 of X. Then player P chooses x_1 in the unit sphere of X_1. Moves alternate thusly, forever. We study this game in the following setting. Certain normalized, 1-unconditional sequences (u_i) and (v_i) are fixed so that S has a winning strategy to force P to select x_i's so that if the moves are (k_1,X_1,x_1,k_2,X_2,x_2,...), then (x_i) is dominated by (u_{k_i}) and/or (x_i) dominates (v_{k_i}). In particular, we show that for suitable (u_i) and (v_i) if X is reflexive and S can win both of the games above, then X embeds into a reflexive space Z with an FDD which also satisfies analogous block upper (u_i) and lower (v_i) estimates. Certain universal space consequences ensue. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 30 pages, uses mypreamble.tex The source file(s), mypreamble.tex: 7670 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0651 or http://arXiv.org/abs/0706.0651 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0651 or in gzipped form by using subject line get 0706.0651 to: math(a)arXiv.org.

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Abstract of a paper by P. Holicky, O. Kalenda, L. Vesely, and L. Zajicek
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "Quotients of continuous convex functions on nonreflexive Banach spaces" by P. Holicky, O. Kalenda, L. Vesely, and L. Zajicek. Abstract: On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction gives also a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. Archive classification: math.FA Mathematics Subject Classification: 46B10; 46B03 Remarks: 5 pages The source file(s), 06HKVZscisly.tex: 19081 bytes, is(are) stored in gzipped form as 0706.0633.gz with size 7kb. The corresponding postcript file has gzipped size 71kb. Submitted from: zajicek(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0633 or http://arXiv.org/abs/0706.0633 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0633 or in gzipped form by using subject line get 0706.0633 to: math(a)arXiv.org.

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Abstract of a paper by James R. Lee, Assaf Naor, and Yuval Peres
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "Trees and Markov convexity" by James R. Lee, Assaf Naor, and Yuval Peres. Abstract: We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant called Markov convexity, and show how it can be used to compute the Euclidean distortion of any metric tree up to universal factors. Archive classification: math.MG math.FA The source file(s), TreeMarkov-GAFA.tex: 228845 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0545 or http://arXiv.org/abs/0706.0545 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0545 or in gzipped form by using subject line get 0706.0545 to: math(a)arXiv.org.

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Abstract of a paper by L. Vesely and L. Zajicek
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "On compositions of d.c. functions and mappings" by L. Vesely and L. Zajicek. Abstract: A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under compositions does not hold in general. However, we prove that it holds in some interesting particular cases. Our main results about compositions are proved in the more general context of d.c. mappings between normed linear spaces. Archive classification: math.FA math.CA Mathematics Subject Classification: 46B99; 26B25; 52A41 Remarks: 19 pages The source file(s), PFzkr13.tex: 57750 bytes, is(are) stored in gzipped form as 0706.0624.gz with size 18kb. The corresponding postcript file has gzipped size 125kb. Submitted from: zajicek(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0624 or http://arXiv.org/abs/0706.0624 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0624 or in gzipped form by using subject line get 0706.0624 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge and Javier Parcet
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "Operator space Lp embedding theory I" by Marius Junge and Javier Parcet. Abstract: Given any $1 < q \le 2$, we use new free probability techniques to construct a completely isomorphic embedding of $\ell_q$ (equipped with its natural operator space structure) into the predual of a sufficiently large QWEP von Neumann algebra. Archive classification: math.OA math.PR Mathematics Subject Classification: 46L07; 46L51; 46L52; 46L54 Remarks: This is the most accessible part of our paper Operator space embedding of Lq into Lp, 28 pages. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0550 or http://arXiv.org/abs/0706.0550 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0550 or in gzipped form by using subject line get 0706.0550 to: math(a)arXiv.org.

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Abstract of a paper by Tim Austin, Assaf Naor, and Alain Valette
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "The Euclidean distortion of the lamplighter group" by Tim Austin, Assaf Naor, and Alain Valette. Abstract: We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion ${\rm O}\left(\sqrt{\log n}\right)$. This matches the lower bound proved by Lee, Naor and Peres in~\cite{LeeNaoPer}, answering a question posed in that paper. Thus the Euclidean distortion of $C_2 \bwr C_n$ is $\Theta\left(\sqrt{\log n}\right)$. Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Euclidean embedding of a finite group can always be chosen to be equivariant, as shown by Aharoni, Maurey and Mityagin~\cite{AhaMauMit} and by Gromov (see~\cite{deCTesVal}), such representation-theoretic considerations suggest a general tool for obtaining upper and lower bounds on Euclidean embeddings of finite groups. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20, 54E40, 52C99 The source file(s), LAMP-official.bbl: 3624 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0705.4662 or http://arXiv.org/abs/0705.4662 or by email in unzipped form by transmitting an empty message with subject line uget 0705.4662 or in gzipped form by using subject line get 0705.4662 to: math(a)arXiv.org.

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Abstract of a paper by Gordan Zitkovic
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "A filtered version of the bipolar theorem of Brannath and Schachermayer" by Gordan Zitkovic. Abstract: We extend the Bipolar Theorem of Brannath and Schachermayer (1999) to the space of nonnegative cadlag supermartingales on a filtered probability space. We formulate the notion of fork-convexity as an analogue to convexity in this setting. As an intermediate step in the proof of our main result we establish a conditional version of the Bipolar theorem. In an application to mathematical finance we describe the structure of the set of dual processes of the utility maximization problem of Kramkov and Schachermayer (1999) and give a budget-constraint characterization of admissible consumption processes in an incomplete semimartingale market. Archive classification: math.PR math.FA Citation: Journal of Theoretical Probability (2005) vol. 15 no. 1 The source file(s), Bipolar.tex: 58142 bytes, is(are) stored in gzipped form as 0706.0049.gz with size 18kb. The corresponding postcript file has gzipped size 101kb. Submitted from: gordanz(a)math.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.0049 or http://arXiv.org/abs/0706.0049 or by email in unzipped form by transmitting an empty message with subject line uget 0706.0049 or in gzipped form by using subject line get 0706.0049 to: math(a)arXiv.org.

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Abstract of a paper by Robert J Taggart
by Dale Alspach 06 Jun '07

06 Jun '07

This is an announcement for the paper "Pointwise convergence for semigroups in vector-valued $L^p$ spaces" by Robert J Taggart. Abstract: Suppose that T_t is a symmetric diffusion semigroup on L^2(X). We show that the tensor extension of T_t to L^p(X;B), where B belongs to a certain class of UMD spaces, exhibits pointwise convergence almost everywhere as t approaches zero. Our principal tools are vector-valued versions of maximal theorems due to Hopf--Dunford--Schwartz and Stein. These are proved using subpositivity and estimates on the bounded imaginary powers of the generator of T_t. An extension of these results to analytic continuations of T_t is also given. Archive classification: math.FA math.SP Mathematics Subject Classification: 47D03 The source file(s), ptwise_convergence_preprint.tex: 67741 bytes, is(are) stored in gzipped form as 0705.4510.gz with size 19kb. The corresponding postcript file has gzipped size 124kb. Submitted from: r.taggart(a)unsw.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0705.4510 or http://arXiv.org/abs/0705.4510 or by email in unzipped form by transmitting an empty message with subject line uget 0705.4510 or in gzipped form by using subject line get 0705.4510 to: math(a)arXiv.org.

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Abstract of a paper by S.S. Kutateladze
by Dale Alspach 30 May '07

30 May '07

This is an announcement for the paper "Interaction of order and convexity" by S.S. Kutateladze. Abstract: This is an overview of merging the techniques of Riesz space theory and convex geometry. Archive classification: math.FA Mathematics Subject Classification: 46B42; 52A39 Remarks: Prepared for the Russian--German geometry meeting dedicated to the The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/ or http://arXiv.org/abs/ or by email in unzipped form by transmitting an empty message with subject line uget or in gzipped form by using subject line get to: math(a)arXiv.org.

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