Banach June 2009

banach@mathdept.okstate.edu

2 participants
19 discussions

Conference in Cleveland, August 1-7, 2010
by Stanislaw J. Szarek 29 Jun '09

29 Jun '09

This is a preliminary announcement of the conference on PERSPECTIVES IN HIGH DIMENSIONS to be held on the campus of Case Western Reserve University in Cleveland, Ohio, U.S.A. from August 1 until August 7, 2010. The aim of the conference is to reflect on recent and future developments in broadly understood geometric functional analysis, with emphasis on interactions with other subfields of mathematics and with other mathematical sciences. The conference will be supported by the NSF via Focused Research Grant which involves CWRU, Kent State University, University of Michigan and University of Missouri (see http://www.math.lsa.umich.edu/research/gfa/index.html). More details will be provided in the coming months; at this point we would like to inform potential participants so that they can "save the date." Should you have any questions, please contact one of the organizers listed below. The temporary conference website is at http://www.cwru.edu/artsci/math/szarek/perspectives/ Alexander Koldobsky <koldobskiya(a)missouri.edu> Mark Rudelson <RudelsonM(a)missouri.edu> Dmitry Ryabogin <ryabogin(a)math.kent.edu> Stanislaw Szarek <szarek(a)cwru.edu> Roman Vershynin <romanv(a)umich.edu> Elisabeth Werner <elisabeth.werner(a)case.edu> Artem Zvavitch <zvavitch(a)math.kent.edu>

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Abstract of a paper by Harald Hanche-Olsen and Helge Holden
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "The Kolmogorov-Riesz compactness theorem" by Harald Hanche-Olsen and Helge Holden. Abstract: We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem. Archive classification: math.CA math.FA Mathematics Subject Classification: 46E30, 46E35; 46N20 The source file(s), kolmogorov.tex: 36412 bytes, is(are) stored in gzipped form as 0906.4883.gz with size 12kb. The corresponding postcript file has gzipped size 213kb. Submitted from: holden(a)math.ntnu.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.4883 or http://arXiv.org/abs/0906.4883 or by email in unzipped form by transmitting an empty message with subject line uget 0906.4883 or in gzipped form by using subject line get 0906.4883 to: math(a)arXiv.org.

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Abstract of a paper by Turdebek N. Bekjan, Zeqian Chen, Mathilde Perrin and Zhi Yin
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales" by Turdebek N. Bekjan, Zeqian Chen, Mathilde Perrin and Zhi Yin. Abstract: We prove that atomic decomposition for the Hardy spaces h_1 and H_1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales h_p and bmo form interpolation scales with respect to both complex and real interpolations. Archive classification: math.OA math.FA Mathematics Subject Classification: 46L53, 46L52 The source file(s), ncatom_interp.tex: 58773 bytes, is(are) stored in gzipped form as 0906.4437.gz with size 16kb. The corresponding postcript file has gzipped size 115kb. Submitted from: mathilde.perrin(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.4437 or http://arXiv.org/abs/0906.4437 or by email in unzipped form by transmitting an empty message with subject line uget 0906.4437 or in gzipped form by using subject line get 0906.4437 to: math(a)arXiv.org.

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Abstract of a paper by Mathilde Perrin
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "A noncommutative Davis' decomposition for martingales" by Mathilde Perrin. Abstract: We prove an analogue of the classical Davis' decomposition for martingales in noncommutative L_p-spaces, involving the square functions. We also determine the dual space of the noncommutative conditioned Hardy space \h_1. We further extend this latter result to the case 1<p<2. Archive classification: math.OA math.FA Mathematics Subject Classification: 46L53, 46L52 (Primary) 46L51, 60G42 (Secondary) Remarks: To be published in Journal of London Math. Soc The source file(s), Nc_davis2.tex: 58260 bytes, is(are) stored in gzipped form as 0906.4434.gz with size 15kb. The corresponding postcript file has gzipped size 118kb. Submitted from: mathilde.perrin(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.4434 or http://arXiv.org/abs/0906.4434 or by email in unzipped form by transmitting an empty message with subject line uget 0906.4434 or in gzipped form by using subject line get 0906.4434 to: math(a)arXiv.org.

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Abstract of a paper by Jin Xi Chen, Zi Li Chen, and Ngai-Ching Wong
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "A Banach-Stone theorem for Riesz isomorphisms of Banach lattices" by Jin Xi Chen, Zi Li Chen, and Ngai-Ching Wong. Abstract: Let $X$ and $Y$ be compact Hausdorff spaces, and $E$, $F$ be Banach lattices. Let $C(X,E)$ denote the Banach lattice of all continuous $E$-valued functions on $X$ equipped with the pointwise ordering and the sup norm. We prove that if there exists a Riesz isomorphism $\mathnormal{\Phi}: C(X,E)\to C(Y,F)$ such that $\mathnormal{\Phi}f$ is non-vanishing on $Y$ if and only if $f$ is non-vanishing on $X$, then $X$ is homeomorphic to $Y$, and $E$ is Riesz isomorphic to $F$. In this case, $\mathnormal{\Phi}$ can be written as a weighted composition operator: $\mathnormal{\Phi} f(y)=\mathnormal{\Pi}(y)(f(\varphi(y)))$, where $\varphi$ is a homeomorphism from $Y$ onto $X$, and $\mathnormal{\Pi}(y)$ is a Riesz isomorphism from $E$ onto $F$ for every $y$ in $Y$. This generalizes some known results obtained recently. Archive classification: math.FA Mathematics Subject Classification: 46B42, 47B65 The source file(s), Chen_Chen_Wong_Banach-Stone_theorem_for_Riesz_isomorphisms.tex: 24807 bytes, is(are) stored in gzipped form as 0906.4196.gz with size 8kb. The corresponding postcript file has gzipped size 71kb. Submitted from: jinxichen(a)home.swjtu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.4196 or http://arXiv.org/abs/0906.4196 or by email in unzipped form by transmitting an empty message with subject line uget 0906.4196 or in gzipped form by using subject line get 0906.4196 to: math(a)arXiv.org.

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Abstract of a paper by Baudier Florent
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Embeddings of proper metric spaces into Banach spaces" by Baudier Florent. Abstract: We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of $\mathcal{L}_{p}$-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any $\mathcal{L}_p$-space into any Banach space $X$ containing the $\ell_p^n$'s. Finally using an argument of G. Schechtman we prove that for general proper metric spaces and for Banach spaces without cotype a converse statement holds. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20; 51F99 Remarks: 16 pages The source file(s), proper.tex: 34599 bytes, is(are) stored in gzipped form as 0906.3696.gz with size 10kb. The corresponding postcript file has gzipped size 91kb. Submitted from: florent.baudier(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.3696 or http://arXiv.org/abs/0906.3696 or by email in unzipped form by transmitting an empty message with subject line uget 0906.3696 or in gzipped form by using subject line get 0906.3696 to: math(a)arXiv.org.

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Abstract of a paper by Daniel Carando and Daniel Galicer
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators" by Daniel Carando and Daniel Galicer. Abstract: We study tensor norms that destroy unconditionality in the following sense: for every Banach space $E$ with unconditional basis, the $n$-fold tensor product of $E$ (with the corresponding tensor norms) does not have unconditional basis. We show that this holds for all injective and projective tensor norms different from $\varepsilon$ and $\pi$, both in the full and symmetric tensor products. In particular, every nontrivial natural symmetric tensor norms destroys unconditionality. We prove that there are exactly 6 natural symmetric tensor norms for $n\ge 3$, a noteworthy difference with the 2-fold case. We present applications to polynomial ideals: we show that many polynomial ideals never have the Gordon-Lewis property or, in the spirit of a result of Defant and Kalton, can have the Gordon-Lewis property but never have unconditional basis. We also consider unconditionality in multilinear and operator ideals. Archive classification: math.FA Mathematics Subject Classification: 46M05; 46G25; 47L20 Remarks: 27 pages The source file(s), Carando-GalicerArxiv.tex: 100018 bytes, is(are) stored in gzipped form as 0906.3253.gz with size 26kb. The corresponding postcript file has gzipped size 163kb. Submitted from: dgalicer(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.3253 or http://arXiv.org/abs/0906.3253 or by email in unzipped form by transmitting an empty message with subject line uget 0906.3253 or in gzipped form by using subject line get 0906.3253 to: math(a)arXiv.org.

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Abstract of a paper by D. Azagra, R. Fry, L. Keener
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Smooth extensions of functions on separable Banach spaces" by D. Azagra, R. Fry, and L. Keener. Abstract: Let $X$ be a Banach space with a separable dual $X^{*}$. Let $Y\subset X$ be a closed subspace, and $f:Y\to\mathbb{R}$ a $C^{1}$-smooth function. Then we show there is a $C^{1}$ extension of $f$ to $X$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 14 pages The source file(s), AFKJune14.tex: 44778 bytes, is(are) stored in gzipped form as 0906.2989.gz with size 14kb. The corresponding postcript file has gzipped size 97kb. Submitted from: dazagra(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.2989 or http://arXiv.org/abs/0906.2989 or by email in unzipped form by transmitting an empty message with subject line uget 0906.2989 or in gzipped form by using subject line get 0906.2989 to: math(a)arXiv.org.

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Abstract of a paper by Anton Baranov and Harald Woracek
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Majorization in de Branges spaces II. Banach spaces generated by majorants" by Anton Baranov and Harald Woracek. Abstract: This is the second part in a series dealing with subspaces of de~Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by admissible majorants. We study their interplay with the original de Branges space structure, and their geometry. In particular, we will show that, generically, they will be nonreflexive and nonseparable. Archive classification: math.CV math.FA Mathematics Subject Classification: 46E15, 46B26, 46E22 The source file(s), sprm5.tex: 84171 bytes, is(are) stored in gzipped form as 0906.2943.gz with size 23kb. The corresponding postcript file has gzipped size 145kb. Submitted from: antonbaranov(a)netscape.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.2943 or http://arXiv.org/abs/0906.2943 or by email in unzipped form by transmitting an empty message with subject line uget 0906.2943 or in gzipped form by using subject line get 0906.2943 to: math(a)arXiv.org.

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Abstract of a paper by Michael Cwikel and Alon Ivtsan
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Counterexamples for interpolation of compact Lipschitz operators" by Michael Cwikel and Alon Ivtsan. Abstract: Let (A_0,A_1) and (B_0,B_1) be Banach couples with A_0 contained in A_1 and B_0 contained in B_1. Let T:A_1 --> B_1 be a possibly nonlinear operator which is a compact Lipschitz map of A_j into B_j for j=0,1. It is known that T maps the Lions-Peetre space (A_0,A_1)_\theta,q boundedly into (B_0,B_1)_\theta,q for each \theta in (0,1) and each q in [1,\infty), and that this map is also compact if if T is linear. We present examples which show that in general the map T:(A_0,A_1)_\theta,q --> (B_0,B_1)_\theta,q is not compact. Archive classification: math.FA Mathematics Subject Classification: 46B70 (primary), 47H99, 46B50 (secondary) Remarks: 22 pages. The main results are on pages 1-8. Later pages contain some additional more elaborate counterexamples The source file(s), 14cCounterexample.tex: 76306 bytes e1e2yellow.jpg: 50818 bytes enen+1yellowgreen.jpg: 102039 bytes etnew.jpg: 65214 bytes newen-yellow.jpg: 56125 bytes, is(are) stored in gzipped form as 0906.2432.tar.gz with size 250kb. The corresponding postcript file has gzipped size . Submitted from: mcwikel(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.2432 or http://arXiv.org/abs/0906.2432 or by email in unzipped form by transmitting an empty message with subject line uget 0906.2432 or in gzipped form by using subject line get 0906.2432 to: math(a)arXiv.org.

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Banach June 2009