Banach June 2007

banach@mathdept.okstate.edu

1 participants
15 discussions

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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Banach June 2007