Banach

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Abstract of a paper by Alexander Koldobsky
by alspach＠fourier.math.okstate.edu 11 Mar '09

11 Mar '09

This is an announcement for the paper "Positive definite functions and multidimensional versions of random variables" by Alexander Koldobsky. Abstract: We say that a random vector $X=(X_1,...,X_n)$ in $R^n$ is an $n$-dimensional version of a random variable $Y$ if for any $a\in R^n$ the random variables $\sum a_iX_i$ and $\gamma(a) Y$ are identically distributed, where $\gamma:R^n\to [0,\infty)$ is called the standard of $X.$ An old problem is to characterize those functions $\gamma$ that can appear as the standard of an $n$-dimensional version. In this paper, we prove the conjecture of Lisitsky that every standard must be the norm of a space that embeds in $L_0.$ This result is almost optimal, as the norm of any finite dimensional subspace of $L_p$ with $p\in (0,2]$ is the standard of an $n$-dimensional version ($p$-stable random vector) by the classical result of P.L\`evy. An equivalent formulation is that if a function of the form $f(\|\cdot\|_K)$ is positive definite on $R^n,$ where $K$ is an origin symmetric star body in $R^n$ and $f:R\to R$ is an even continuous function, then either the space $(R^n,\|\cdot\|_K)$ embeds in $L_0$ or $f$ is a constant function. Combined with known facts about embedding in $L_0,$ this result leads to several generalizations of the solution of Schoenberg's problem on positive definite functions. Archive classification: math.PR math.FA Mathematics Subject Classification: 60E05 The source file(s), posdef1.tex: 32112 bytes, is(are) stored in gzipped form as 0903.1433.gz with size 10kb. The corresponding postcript file has gzipped size 86kb. Submitted from: koldobskiya(a)missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.1433 or http://arXiv.org/abs/0903.1433 or by email in unzipped form by transmitting an empty message with subject line uget 0903.1433 or in gzipped form by using subject line get 0903.1433 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 11 Mar '09

11 Mar '09

This is an announcement for the paper "Weakly countably determined spaces of high complexity" by Antonio Aviles. Abstract: We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets. Therefore the Banach spaces constructed by means of these families have at most coanalytic complexity. Archive classification: math.FA Mathematics Subject Classification: 46B26 Citation: Stud. Math. 185, No. 3, 291-303 (2008) Remarks: This version differs from the published in Studia Mathematica in that The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0852 or http://arXiv.org/abs/0903.0852 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0852 or in gzipped form by using subject line get 0903.0852 to: math(a)arXiv.org.

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Abstract of a paper by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda
by alspach＠fourier.math.okstate.edu 11 Mar '09

11 Mar '09

This is an announcement for the paper "Cotype and absolutely summing linear operators" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: Cotype is used in this paper to prove new results concerning the existence of non-absolutely summing linear operators between Banach spaces. We derive consequences that extend/generalize/ complement some classic results. We also point out that some of our results are sharp. Archive classification: math.FA Mathematics Subject Classification: 46G25, 45B20 Remarks: 8 pages The source file(s), linear_results03March2009-without.tex: 40121 bytes, is(are) stored in gzipped form as 0903.0583.gz with size 12kb. The corresponding postcript file has gzipped size 78kb. Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0583 or http://arXiv.org/abs/0903.0583 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0583 or in gzipped form by using subject line get 0903.0583 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles, Bernardo Cascales, Vladimir Kadets, and Alexander Leonov
by alspach＠fourier.math.okstate.edu 11 Mar '09

11 Mar '09

This is an announcement for the paper "The Schur l1 Theorem for filters" by Antonio Aviles, Bernardo Cascales, Vladimir Kadets, and Alexander Leonov. Abstract: We study the classes of filters F on N such that the weak and strong F-convergence of sequences in l1 coincide. We study also an analogue of l1 weak sequential completeness theorem for filter convergence. Archive classification: math.FA math.GN Citation: Journal of Mathematical Physics, Analysis, Geometry: 2007, v. 3, The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0659 or http://arXiv.org/abs/0903.0659 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0659 or in gzipped form by using subject line get 0903.0659 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles and Yolanda Moreno
by alspach＠fourier.math.okstate.edu 11 Mar '09

11 Mar '09

This is an announcement for the paper "Automorphisms in spaces of continuous functions on Valdivia compacta" by Antonio Aviles and Yolanda Moreno. Abstract: We show that there are no automorphic Banach spaces of the form C(K) with K continuous image of Valdivia compact except the spaces c0(I). Nevertheless, when K is an Eberlein compact of finite height such that C(K) is not isomorphic to c0(I), all isomorphism between subspaces of C(K) of size less than aleph_omega extend to automorphisms of C(K). Archive classification: math.FA math.GN Mathematics Subject Classification: 46B26 Citation: Topology Appl. 155, No. 17-18, 2027-2030 (2008) The source file(s), AutomorficosValdivia.tex: 19190 bytes, is(are) stored in gzipped form as 0903.0658.gz with size 7kb. The corresponding postcript file has gzipped size 61kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0658 or http://arXiv.org/abs/0903.0658 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0658 or in gzipped form by using subject line get 0903.0658 to: math(a)arXiv.org.

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Abstract of a paper by M.I. Ostrovskii
by alspach＠fourier.math.okstate.edu 11 Mar '09

11 Mar '09

This is an announcement for the paper "Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert space" by M.I. Ostrovskii. Abstract: The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infinite locally finite graphs excluding a minor embed coarsely into a Hilbert space. In an appendix a direct proof of the latter result is given. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20; 05C12; 54E35 The source file(s), ExpansionArXivversion.tex: 22813 bytes, is(are) stored in gzipped form as 0903.0607.gz with size 8kb. The corresponding postcript file has gzipped size 80kb. Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0607 or http://arXiv.org/abs/0903.0607 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0607 or in gzipped form by using subject line get 0903.0607 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 11 Mar '09

11 Mar '09

This is an announcement for the paper "Countable products of spaces of finite sets" by Antonio Aviles. Abstract: We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification. Archive classification: math.GN math.FA Mathematics Subject Classification: 46B50, 46B26, 54B10, 54D30 Citation: Fundamenta Math. 186, No. 2, 147-159 (2005) The source file(s), SigmakProducts.tex: 40152 bytes, is(are) stored in gzipped form as 0903.0068.gz with size 12kb. The corresponding postcript file has gzipped size 102kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0068 or http://arXiv.org/abs/0903.0068 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0068 or in gzipped form by using subject line get 0903.0068 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "The number of weakly compact sets which generate a Banach space" by Antonio Aviles. Abstract: We consider the cardinal invariant CG(X) of the minimal number of weakly compact subsets which generate a Banach space X. We study the behavior of this index when passing to subspaces, its relation with the Lindelof number in the weak topology and other related questions. Archive classification: math.FA math.GN Citation: Israel J. Math. 159, 189-204 (2007) The source file(s), CGX.tex: 47171 bytes, is(are) stored in gzipped form as 0903.0063.gz with size 15kb. The corresponding postcript file has gzipped size 94kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0063 or http://arXiv.org/abs/0903.0063 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0063 or in gzipped form by using subject line get 0903.0063 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "The number of weakly compact convex subsets of the Hilbert space" by Antonio Aviles. Abstract: We prove that for k an uncountable cardinal, there exist 2^k many non homeomorphic weakly compact convex subsets of weight k in the Hilbert space of density k. Archive classification: math.GN math.FA Mathematics Subject Classification: 54B35, 52A07 Citation: Topology Appl. 155, No. 15, 1720-1725 (2008) The source file(s), Manyconvex.tex: 28889 bytes, is(are) stored in gzipped form as 0903.0163.gz with size 9kb. The corresponding postcript file has gzipped size 71kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0163 or http://arXiv.org/abs/0903.0163 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0163 or in gzipped form by using subject line get 0903.0163 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "Renormings of the dual of James tree spaces" by Antonio Aviles. Abstract: We discuss renorming properties of the dual of a James tree space JT. We present examples of weakly Lindelof determined JT such that JT* admits neither strictly convex nor Kadec renorming and of weakly compactly generated JT such that JT* does not admit Kadec renorming although it is strictly convexifiable. Archive classification: math.FA Mathematics Subject Classification: 46B26 Citation: Bull. Lond. Math. Soc. 39, No. 2, 221-231 (2007) The source file(s), RosenthalLUR.tex: 41974 bytes, is(are) stored in gzipped form as 0903.0158.gz with size 13kb. The corresponding postcript file has gzipped size 91kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0158 or http://arXiv.org/abs/0903.0158 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0158 or in gzipped form by using subject line get 0903.0158 to: math(a)arXiv.org.

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