August 2011 - Banach - mathdept.okstate.edu

Abstract of a paper by Denka Kutzarova, Antonis Manoussakis, and Anna Pelczar-Barwacz
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Isomorphisms and strictly singular operators in mixed Tsirelson spaces" by Denka Kutzarova, Antonis Manoussakis, and Anna Pelczar-Barwacz. Abstract: We study the family of isomorphisms and strictly singular operators in mixed Tsirelson spaces and their modified versions setting. We show sequential minimality of modified mixed Tsirelson spaces $T_M[(\mc{S}_n,\theta_n)]$ satisfying some regularity conditions and present results on existence of strictly singular non-compact operators on subspaces of mixed Tsirelson spaces defined by the families $(\mc{A}_n)_n$ and $(\mc{S}_n)_n$. Archive classification: math.FA Remarks: 29 pages, no figures Submitted from: amanousakis(a)isc.tuc.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.2810 or http://arXiv.org/abs/1107.2810

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Abstract of a paper by Sonja Cox and Mark Veraar
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Vector-valued decoupling and the Burkholder-Davis-Gundy inequality" by Sonja Cox and Mark Veraar. Abstract: Let X be a Banach space. We prove p-independence of the one-sided decoupling inequality for X-valued tangent martingales as introduced by Kwapien and Woyczynski. It is known that a Banach space X satisfies the two-sided decoupling inequality if and only if X is a UMD Banach space. The one-sided decoupling inequality is a weaker property, including e.g. the space L^1. We provide information on the optimal constants for various spaces, and give a upper estimate of order p in general. In the second part of our paper we derive Burkholder-Davis-Gundy type estimates for p-th moments, p in (0,infty), of X-valued stochastic integrals, provided X is a UMD Banach space or a space in which the one-sided decoupling inequality holds. Archive classification: math.FA Remarks: To appear in the Illinois Journal of Mathematics Submitted from: sonja.cox(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.2218 or http://arXiv.org/abs/1107.2218

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Abstract of a paper by David Alonso-Gutierrez, Jesus Bastero and Julio Bernues
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Factoring Sobolev inequalities through classes of functions" by David Alonso-Gutierrez, Jesus Bastero and Julio Bernues. Abstract: We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp) connection between them. Archive classification: math.FA Mathematics Subject Classification: 46E35, 46E30, 26D10, 52A40 Submitted from: bernues(a)unizar.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.2139 or http://arXiv.org/abs/1107.2139

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Abstract of a paper by Nir Lev and Alexander Olevskii
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon" by Nir Lev and Alexander Olevskii. Abstract: Wiener characterized the cyclic vectors (with respect to translations) in $l^p(Z)$ and $L^p(R)$, $p=1,2$, in terms of the zero set of the Fourier transform. He conjectured that a similar characterization should be true for $1<p<2$. Our main result contradicts this conjecture. Archive classification: math.CA math.FA Mathematics Subject Classification: 42A63 (Primary) 43A45, 47A16 (Secondary) Citation: Annals of Mathematics 174 (2011), 519-541 Submitted from: levnir(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.0447 or http://arXiv.org/abs/0908.0447

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Abstract of a paper by Piotr Wilczek
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Some representation theorem for nonreflexive Banach space ultrapowers under the Continuum Hypothesis" by Piotr Wilczek. Abstract: In this paper it will be shown that assuming the Continuum Hypothesis (CH) every nonreflexive Banach space ultrapower is isometrically isomorphic to the space of continuous, bounded and real-valued functions on the Parovicenko space. This Representation Theorem will be helpful in proving some facts from geometry and topology of nonreflexive Banach space ultrapowers. Archive classification: math.LO math.FA Mathematics Subject Classification: 46B08, 46B20, 46B25 Remarks: 12 pages Submitted from: edwil(a)mail.icpnet.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.1693 or http://arXiv.org/abs/1107.1693

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Abstract of a paper by Piotr Wilczek
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Under the Continuum Hypothesis all nonreflexive Banach space ultrapowers are primary" by Piotr Wilczek. Abstract: In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive Banach space is always primary. Consequently, any infinite dimensional nonsuperreflexive Banach space can be isometrically embedded into its primary ultrapowers. Archive classification: math.LO math.FA Mathematics Subject Classification: 46B08, 46B20, 46B25 Remarks: 7 pages Submitted from: edwil(a)mail.icpnet.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.1692 or http://arXiv.org/abs/1107.1692

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Abstract of a paper by Silvia Lassalle and Pablo Turco
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "On p-compact mappings and p-approximation" by Silvia Lassalle and Pablo Turco. Abstract: The notion of $p$-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of $p$-approximation property and $p$-compact operators, which form a ideal with its ideal norm $\kappa_p$. This paper examines the interaction between the $p$-approximation property and the space of holomorphic functions. Here, the $p$-compact analytic functions play a crucial role. In order to understand this type of functions we define a $p$-compact radius of convergence which allow us to give a characterization of the functions in the class. We show that $p$-compact holomorphic functions behave more like nuclear than compact maps. We use the $\epsilon$-product, defined by Schwartz, to characterize the $p$-approximation property of a Banach space in terms of $p$-compact homogeneous polynomials and also in terms of $p$-compact holomorphic functions with range on the space. Finally, we show that $p$-compact holomorphic functions fit in the framework of holomorphy types which allows us to inspect the $\kappa_p$-approximation property. Along these notes we solve several questions posed by Aron, Maestre and Rueda. Archive classification: math.FA Mathematics Subject Classification: 46G20, 46B28 Remarks: 31 pages Submitted from: pabloaturco(a)yahoo.com.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.1670 or http://arXiv.org/abs/1107.1670

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Abstract of a paper by Piotr W. Nowak
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Poincar\'e inequalities and rigidity for actions on Banach spaces" by Piotr W. Nowak. Abstract: The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present conditions implying that every affine isometric action of a given group $G$ on a reflexive Banach space $X$ has a fixed point. This last property is a strong version of Kazhdan's property (T) and is equivalent to the fact that $H^1(G,\pi)=0$ for every isometric representation $\pi$ of $G$ on $X$. We give examples of groups for which every affine isometric action on an $L_p$ space has a fixed point for certain $p>2$, and present several applications. In particular, we give a lower bound on the conformal dimension of the boundary of a hyperbolic group in the Gromov density model. Archive classification: math.GR math.FA math.OA Submitted from: pnowak(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.1896 or http://arXiv.org/abs/1107.1896

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