Banach March 2009

banach@mathdept.okstate.edu

4 participants
29 discussions

Abstract of a paper by Spiros A Argyros and Richard G Haydon
by alspach＠fourier.math.okstate.edu 28 Mar '09

28 Mar '09

This is an announcement for the paper "A hereditarily indecomposable L_\infty-space that solves the scalar-plus-compact problem" by Spiros A Argyros and Richard G Haydon. Abstract: We construct a hereditarily indecomposable Banach space with dual isomorphic to $\ell_1$. Every bounded linear operator on this space has the form $\lambda I+K$ with $\lambda$ a scalar and $K$ compact. Archive classification: math.FA Mathematics Subject Classification: 46B45 The source file(s), BD.tex: 14514 bytes Background.tex: 8660 bytes ConcRem.tex.bak: 13883 bytes Constr.tex: 14452 bytes HIDuals.tex: 12435 bytes Intro.tex: 3383 bytes Operators.tex: 9684 bytes RIS.tex: 22263 bytes ScalarPlusCompact.tex: 8259 bytes ellOneExact.tex: 15439 bytes, is(are) stored in gzipped form as 0903.3921.tar.gz with size 39kb. The corresponding postcript file has gzipped size 191kb. Submitted from: richard.haydon(a)bnc.ox.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.3921 or http://arXiv.org/abs/0903.3921 or by email in unzipped form by transmitting an empty message with subject line uget 0903.3921 or in gzipped form by using subject line get 0903.3921 to: math(a)arXiv.org.

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Abstract of a paper by Vesko Valov
by alspach＠fourier.math.okstate.edu 28 Mar '09

28 Mar '09

This is an announcement for the paper "Linear operators with compact supports, probability measures and Milyutin maps" by Vesko Valov. Abstract: The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and k-metrizability, are preserved under Milyutin maps. Archive classification: math.GN math.FA Mathematics Subject Classification: 28A33; 54C10 Remarks: 26 pages The source file(s), Milutin.TEX: 91700 bytes, is(are) stored in gzipped form as 0903.3435.gz with size 25kb. The corresponding postcript file has gzipped size 141kb. Submitted from: veskov(a)nipissingu.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.3435 or http://arXiv.org/abs/0903.3435 or by email in unzipped form by transmitting an empty message with subject line uget 0903.3435 or in gzipped form by using subject line get 0903.3435 to: math(a)arXiv.org.

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Abstract of a paper by Hamed Hatami
by alspach＠fourier.math.okstate.edu 28 Mar '09

28 Mar '09

This is an announcement for the paper "On generalizations of Gowers norms and their geometry" by Hamed Hatami. Abstract: Motivated by the definition of the Gowers uniformity norms, we introduce and study a wide class of norms. Our aim is to establish them as a natural generalization of the $L_p$ norms. We shall prove that these normed spaces share many of the nice properties of the $L_p$ spaces. Some examples of these norms are $L_p$ norms, trace norms $S_p$ when $p$ is an even integer, and Gowers uniformity norms. Every such norm is defined through a pair of weighted hypergraphs. In regard to a question of Laszlo Lovasz, we prove several results in the direction of characterizing all hypergraph pairs that correspond to norms. Archive classification: math.CO math.FA Mathematics Subject Classification: 46B20, 46E30, 05D99 Remarks: 29 pages The source file(s), arxiv/ProductNorm17.bbl: 3969 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.3237 or http://arXiv.org/abs/0903.3237 or by email in unzipped form by transmitting an empty message with subject line uget 0903.3237 or in gzipped form by using subject line get 0903.3237 to: math(a)arXiv.org.

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Abstract of a paper by Humberto Rafeiro
by alspach＠fourier.math.okstate.edu 28 Mar '09

28 Mar '09

This is an announcement for the paper "Kolmogorov compactness criterion in variable exponent Lebesgue spaces" by Humberto Rafeiro. Abstract: The well-known Kolmogorov compactness criterion is extended to the case of variable exponent Lebesgue spaces $L^{p(\cdot)}(\overline{\Omega})$, where $\Omega$ is a bounded open set in $\mathbb R^n$ and $p(\cdot)$ satisfies some ``standard'' conditions. Our final result should be called Kolmogorov-Tulajkov Sudakov compactness criterion, since it includes the case $p_-=1$ and requires only the ``uniform'' condition. Archive classification: math.FA Mathematics Subject Classification: 46B50, 46E30 Remarks: 8 pages The source file(s), kolmogorov_18_03_2009.tex: 23807 bytes, is(are) stored in gzipped form as 0903.3214.gz with size 8kb. The corresponding postcript file has gzipped size 76kb. Submitted from: hrafeiro(a)ualg.pt The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.3214 or http://arXiv.org/abs/0903.3214 or by email in unzipped form by transmitting an empty message with subject line uget 0903.3214 or in gzipped form by using subject line get 0903.3214 to: math(a)arXiv.org.

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Workshop at A&M
by Bill Johnson 20 Mar '09

20 Mar '09

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2009 The Summer 2009 Workshop in Analysis and Probability at Texas A&M University will be in session from July 7 until August 13. For information about the Workshop, consult the Workshop Home Page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 7-9. Rafal Latala, Assaf Naor, and Grigoris Paouris (chair) are organizing a Concentration Week on "Probability in Asymptotic Geometry" for the week of July 20-24. This Concentration Week will focus on high dimensional phenomena concerning convex bodies, random polytopes, and random matrices. These topics lie in the intersection of probability, analysis, geometry, and combinatorics. The goal is to expose the huge variety of techniques used in the study of these objects and to explore the connections between them. Marius Junge, Jesse Peterson, and Gilles Pisier (chair) are organizing a Concentration Week on "Operator Spaces and Approximation Properties of Discrete Groups" for the week of August 3-7. Particular emphasis will be taken to tie together recent results from the theory of von Neumann algebras with operator space ideas. The intention is to provide a background for common points of interest from different perspectives through courses on operator spaces and Dirichlet forms in von Neumann algebras. The intention of this concentration week is to attract attention of younger researchers and students to these new openings The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara(a)math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu>, David Larson <larson(a)math.tamu.edu>, Gilles Pisier <pisier(a)math.tamu.edu>, or Joel Zinn <jzinn(a)math.tamu.edu>. For information about the Concentration Week "Probability in Asymptotic Geometry" contact Grigoris Paouris <grigoris(a)math.tamu.edu>. For information about the Concentration Week on "Operator Spaces and Approximation Properties of Discrete Groups", contact Gilles Pisier <pisier(a)math.tamu.edu>.

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Abstract of a paper by D.Apatsidis, S.A.Argyros, and V.Kanellopoulos
by alspach＠fourier.math.okstate.edu 19 Mar '09

19 Mar '09

This is an announcement for the paper "Hausdorff measures and functions of bounded quadratic variation" by D.Apatsidis, S.A.Argyros, and V.Kanellopoulos. Abstract: To each function $f$ in the space $V_2$ we associate a Hausdorff measure $\mu_f$. We show that the map $f\to\mu_f$ is locally Lipschitz and onto the positive cone of $\mathcal{M}[0,1]$. We use the measures $\{\mu_f:f\in V_2\}$ to determine the structure of the subspaces of $V_2^0$ which either contain $c_0$ or the square stopping time space $S^2$. Archive classification: math.FA Mathematics Subject Classification: 28A78, 46B20, 46B26 Remarks: 36 pages The source file(s), haus_quad2.tex: 141123 bytes, is(are) stored in gzipped form as 0903.2809.gz with size 38kb. The corresponding postcript file has gzipped size 219kb. Submitted from: sargyros(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.2809 or http://arXiv.org/abs/0903.2809 or by email in unzipped form by transmitting an empty message with subject line uget 0903.2809 or in gzipped form by using subject line get 0903.2809 to: math(a)arXiv.org.

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Abstract of a paper by Miguel Martin, Javier Meri, and Mikhail Popov
by alspach＠fourier.math.okstate.edu 19 Mar '09

19 Mar '09

This is an announcement for the paper "On the numerical index of real $L_p(\mu)$-spaces" by Miguel Martin, Javier Meri, and Mikhail Popov. Abstract: We give a lower bound for the numerical index of the real space $L_p(\mu)$ showing, in particular, that it is non-zero for $p\neq 2$. In other words, it is shown that for every bounded linear operator $T$ on the real space $L_p(\mu)$, one has $$ \sup\left\{\Bigl|\int |x|^{p-1}\sign(x)\,T x\ d\mu \Bigr|\ : \ x\in L_p(\mu),\,\|x\|=1\right\} \geq \frac{M_p}{8\e}\|T\| $$ where $\displaystyle M_p=\max_{t\in[0,1]}\frac{|t^{p-1}-t|}{1+t^p}>0$ for every $p\neq 2$. It is also shown that for every bounded linear operator $T$ on the real space $L_p(\mu)$, one has $$ \sup\left\{\int |x|^{p-1}|Tx|\ d\mu \ : \ x\in L_p(\mu),\,\|x\|=1\right\} \geq \frac{1}{2\e}\|T\|. $$ Archive classification: math.FA math.OA Mathematics Subject Classification: 46B04, 46E30, 47A12 The source file(s), MartinMeriPopov.tex: 21471 bytes, is(are) stored in gzipped form as 0903.2704.gz with size 7kb. The corresponding postcript file has gzipped size 74kb. Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.2704 or http://arXiv.org/abs/0903.2704 or by email in unzipped form by transmitting an empty message with subject line uget 0903.2704 or in gzipped form by using subject line get 0903.2704 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles and Stevo Todorcevic
by alspach＠fourier.math.okstate.edu 19 Mar '09

19 Mar '09

This is an announcement for the paper "Zero subspaces of polynomials on l1(Gamma)" by Antonio Aviles and Stevo Todorcevic. Abstract: We provide two examples of complex homogeneous quadratic polynomials P on Banach spaces of the form l_1(I). The first polynomial P has both separable and nonseparable maximal zero subspaces. The second polynomial P has the property that while the index-set I is not countable, all zero subspaces of P are separable. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B26, 47H60 Citation: J. Math. Anal. Appl. 350, No. 2, 427-435 (2009) Remarks: Published in special issue dedicated to Isaac Namioka The source file(s), polynomials3.tex: 39718 bytes, is(are) stored in gzipped form as 0903.2374.gz with size 13kb. The corresponding postcript file has gzipped size 89kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.2374 or http://arXiv.org/abs/0903.2374 or by email in unzipped form by transmitting an empty message with subject line uget 0903.2374 or in gzipped form by using subject line get 0903.2374 to: math(a)arXiv.org.

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Abstract of a paper by George Costakis and Antonios Manoussos
by alspach＠fourier.math.okstate.edu 19 Mar '09

19 Mar '09

This is an announcement for the paper "J-class operators and hypercyclicity" by George Costakis and Antonios Manoussos. Abstract: The purpose of the present work is to treat a new notion related to linear dynamics, which can be viewed as a ``localization" of the notion of hypercyclicity. In particular, let $T$ be a bounded linear operator acting on a Banach space $X$ and let $x$ be a non-zero vector in $X$ such that for every open neighborhood $U\subset X$ of $x$ and every non-empty open set $V\subset X$ there exists a positive integer $n$ such that $T^{n}U\cap V\neq\emptyset$. In this case $T$ will be called a $J$-class operator. We investigate the class of operators satisfying the above property and provide various examples. It is worthwhile to mention that many results from the theory of hypercyclic operators have their analogues in this setting. For example we establish results related to the Bourdon-Feldman theorem and we characterize the $J$-class weighted shifts. We would also like to stress that even non-separable Banach spaces which do not support topologically transitive operators, as for example $l^{\infty}(\mathbb{N})$, do admit $J$-class operators. Archive classification: math.FA math.DS Mathematics Subject Classification: 47A16 (primary); 37B99, 54H20 (secondary) Remarks: 21 pages The source file(s), manoussos_jclass.tex: 62003 bytes, is(are) stored in gzipped form as 0704.3354.gz with size 16kb. The corresponding postcript file has gzipped size 116kb. Submitted from: aman(a)math.uoc.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0704.3354 or http://arXiv.org/abs/0704.3354 or by email in unzipped form by transmitting an empty message with subject line uget 0704.3354 or in gzipped form by using subject line get 0704.3354 to: math(a)arXiv.org.

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Abstract of a paper by Delio Mugnolo and Robin Nittka
by alspach＠fourier.math.okstate.edu 19 Mar '09

19 Mar '09

This is an announcement for the paper "Properties of representations of operators acting between spaces of vector-valued functions" by Delio Mugnolo and Robin Nittka. Abstract: A well-known result going back to the 1930s states that all bounded linear operators mapping scalar-valued $L^1$-spaces into $L^\infty$-spaces are kernel operators and that in fact this relation induces an isometric isomorphism between those operators and the space of all bounded kernels. We extend this result to the case of spaces of vector-valued functions. A recent result due to Arendt and Thomaschewski states that the local operators acting on $L^p$-spaces of functions with values in separable spaces are precisely the multiplication operators. We extend this result to non-separable dual spaces. Moreover, we relate positivity and other order properties of the operators to corresponding properties of the representations. Archive classification: math.FA Mathematics Subject Classification: 46G10, 47B34, 46M10, 47B65 Remarks: 13 pages The source file(s), dunfordpettis.bbl: 5993 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.2038 or http://arXiv.org/abs/0903.2038 or by email in unzipped form by transmitting an empty message with subject line uget 0903.2038 or in gzipped form by using subject line get 0903.2038 to: math(a)arXiv.org.

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Banach March 2009