- Banach - mathdept.okstate.edu

Abstract of a paper by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazza
by alspach＠fourier.math.okstate.edu 01 May '09

01 May '09

This is an announcement for the paper "Weak compactness and Orlicz spaces" by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazza. Abstract: We give new proofs that some Banach spaces have Pe{\l}czy\'nski's property $(V)$. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46E30 Citation: Colloquium Mathematicum 112, 1 (2008) 23 - 32 The source file(s), propV-CM.tex: 28111 bytes, is(are) stored in gzipped form as 0904.2970.gz with size 10kb. The corresponding postcript file has gzipped size 77kb. Submitted from: daniel.li(a)euler.univ-artois.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.2970 or http://arXiv.org/abs/0904.2970 or by email in unzipped form by transmitting an empty message with subject line uget 0904.2970 or in gzipped form by using subject line get 0904.2970 to: math(a)arXiv.org.

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Abstract of a paper by David Alonso-Gutierrez, Jesus Bastero, Julio Bernues, and Pawel Wolff
by alspach＠fourier.math.okstate.edu 01 May '09

01 May '09

This is an announcement for the paper "On the isotropy constant of projections of polytopes" by David Alonso-Gutierrez, Jesus Bastero, Julio Bernues, and Pawel Wolff. Abstract: The isotropy constant of any $d$-dimensional polytope with $n$ vertices is bounded by $C \sqrt{\frac{n}{d}}$ where $C>0$ is a numerical constant. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20 (Primary), 52A40, 52A39 (Secondary) The source file(s), ABBW11-arxiv.tex: 43561 bytes, is(are) stored in gzipped form as 0904.2632.gz with size 14kb. The corresponding postcript file has gzipped size 109kb. Submitted from: pawel.wolff(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.2632 or http://arXiv.org/abs/0904.2632 or by email in unzipped form by transmitting an empty message with subject line uget 0904.2632 or in gzipped form by using subject line get 0904.2632 to: math(a)arXiv.org.

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Abstract of a paper by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza
by alspach＠fourier.math.okstate.edu 01 May '09

01 May '09

This is an announcement for the paper "On some random thin sets of integers" by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza. Abstract: We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in {\sl Some new thin sets of integers in Harmonic Analysis, Journal d'Analyse Math\'ematique 86 (2002), 105--138}, namely that there exist $\frac{4}{3}$-Rider sets which are sets of uniform convergence and $\Lambda (q)$-sets for all $q < \infty $, but which are not Rosenthal sets. In a second part, we show, using an older result of Kashin and Tzafriri that, for $p > \frac{4}{3}$, the $p$-Rider sets which we had constructed in that paper are almost surely ot of uniform convergence. Archive classification: math.FA Mathematics Subject Classification: 43 A 46 ; 42 A 55 ; 42 A 61 Citation: Proceedings of the American Mathematical Society 136, 1 (2008) 141 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.2507 or http://arXiv.org/abs/0904.2507 or by email in unzipped form by transmitting an empty message with subject line uget 0904.2507 or in gzipped form by using subject line get 0904.2507 to: math(a)arXiv.org.

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Abstract of a paper by V. Kanellopoulos and K. Tyros
by alspach＠fourier.math.okstate.edu 01 May '09

01 May '09

This is an announcement for the paper "A discretized approach to W.T. Gowers' game" by V. Kanellopoulos and K. Tyros. Abstract: We give an alternative proof of W.T. Gowers' theorem on block bases in Banach spaces by reducing it to a discrete analogue on specific countable nets. Archive classification: math.FA math.CO Mathematics Subject Classification: 05D10, 46B03 Remarks: 12 pages The source file(s), discrgame.tex: 54985 bytes, is(are) stored in gzipped form as 0904.2313.gz with size 15kb. The corresponding postcript file has gzipped size 107kb. Submitted from: ktyros(a)central.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.2313 or http://arXiv.org/abs/0904.2313 or by email in unzipped form by transmitting an empty message with subject line uget 0904.2313 or in gzipped form by using subject line get 0904.2313 to: math(a)arXiv.org.

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Abstract of a paper by Christopher King and Nilufer Koldan
by alspach＠fourier.math.okstate.edu 01 May '09

01 May '09

This is an announcement for the paper "Comparison of matrix norms on bipartite spaces" by Christopher King and Nilufer Koldan. Abstract: Two non-commutative versions of the classical L^q(L^p) norm on the algebra of (mn)x(mn) matrices are compared. The first norm was defined recently by Carlen and Lieb, as a byproduct of their analysis of certain convex functions on matrix spaces. The second norm was defined by Pisier and others using results from the theory of operator spaces. It is shown that the second norm is upper bounded by a constant multiple of the first for all 1 <= p <= 2, q >= 1. In one case (2 = p < q) it is also shown that there is no such lower bound, and hence that the norms are inequivalent. It is conjectured that the norms are inequivalent in all cases. Archive classification: math.FA Remarks: 25 pages The source file(s), 2normsv17.tex: 44891 bytes, is(are) stored in gzipped form as 0904.1710.gz with size 13kb. The corresponding postcript file has gzipped size 109kb. Submitted from: king(a)neu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.1710 or http://arXiv.org/abs/0904.1710 or by email in unzipped form by transmitting an empty message with subject line uget 0904.1710 or in gzipped form by using subject line get 0904.1710 to: math(a)arXiv.org.

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NBFAS + Graham Jameson Meeting 25-26 May 2009
by Niels Jakob Laustsen 23 Apr '09

23 Apr '09

The Department of Mathematics and Statistics at Lancaster University, UK, will host two meetings with a common theme of Banach spaces on 25-26 May 2009. The first, starting after lunch on Monday 25th May, is a meeting of the North British Functional Analysis Seminar (NBFAS); the NBFAS speaker is Stephen J. Dilworth (South Carolina, USA). The second meeting, on Tuesday 26th May, is in honour of GrahamJameson on the occasion of his retirement, celebrating his many significant contributions to the department and the wider mathematical community during his 35-year career in Lancaster. There will be six invited one-hour talks given by the following speakers: - Timothy Feeman (Villanova, USA), - Richard Haydon (Oxford, UK), - Rafal Latala (Warsaw, Poland), - Edward W. Odell, (Texas, USA), - Charles J. Read (Leeds, UK), and - Thomas Schlumprecht (Texas A&M, USA). This meeting is supported by a London Mathematical Society Scheme 1 conference grant. There is support available for UK graduate students; the deadline for applications for such support is 1st May. Full details of both meetings (including registration, schedule, travel and accommodation) can be found at http://www.maths.lancs.ac.uk/jameson For more information, please contact the organizer Niels J. Laustsen (email: n.laustsen(a)lancaster.ac.uk)

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Abstract of a paper by Daniel Freeman, Edward Odell, and Thomas Schlumprecht
by alspach＠fourier.math.okstate.edu 07 Apr '09

07 Apr '09

This is an announcement for the paper "The universality of $\ell_1$ as a dual space" by Daniel Freeman, Edward Odell, and Thomas Schlumprecht. Abstract: Let $X$ be a Banach space with a separable dual. We prove that $X$ embeds isomorphically into a $\L_\infty$ space $Z$ whose dual is isomorphic to $\ell_1$. If $X$ has a shrinking finite dimensional decomposition and $X^*$ does not contain an isomorph of $\ell_1$, then we construct such a $Z$, as above, not containing an isomorph of $c_0$.If $X$ is separable and reflexive, we show that $Z$ can be made to be somewhat reflexive. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 33 pages The source file(s), fos3.tex: 130106 bytes, is(are) stored in gzipped form as 0904.0462.gz with size 37kb. The corresponding postcript file has gzipped size 218kb. Submitted from: schlump(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.0462 or http://arXiv.org/abs/0904.0462 or by email in unzipped form by transmitting an empty message with subject line uget 0904.0462 or in gzipped form by using subject line get 0904.0462 to: math(a)arXiv.org.

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Abstract of a paper by Joel H. Shapiro
by alspach＠fourier.math.okstate.edu 07 Apr '09

07 Apr '09

This is an announcement for the paper "Eigenfunctions for hyperbolic rcmposition roerators---redux" by Joel H. Shapiro. Abstract: The Invariant Subspace Problem (``ISP'') for Hilbert space operators is known to be equivalent to a question that, on its surface, seems surprisingly concrete: For composition operators induced on the Hardy space H^2 by hyperbolic automorphisms of the unit disc, is every nontrivial minimal invariant subspace one dimensional (i.e., spanned by an eigenvector)? In the hope of reviving interest in the contribution this remarkable result might offer to the studies of both composition operators and the ISP, I revisit some known results, weaken their hypotheses and simplify their proofs. Sample results: If f is a hyperbolic disc automorphism with fixed points at a and b (both necessarily on the unit circle), and C_f the composition operator it induces on H^2, then for every function g in the subspace [{(z-a)(z-a)]^(1/2)H^2, the doubly C_f-cyclic subspace generated by g contains many independent eigenvectors; more precisely, the point spectrum of C_f's restriction to that subspace intersects the unit circle in a set of positive measure. Moreover, this restriction of C_f is hypercyclic (some forward orbit is dense). Archive classification: math.FA math.CV Mathematics Subject Classification: 47B33; 47A15 Remarks: 14 pages The source file(s), shapiro_eigenfns_rvsd.tex: 50277 bytes, is(are) stored in gzipped form as 0904.0022.gz with size 15kb. The corresponding postcript file has gzipped size 98kb. Submitted from: joels314(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0904.0022 or http://arXiv.org/abs/0904.0022 or by email in unzipped form by transmitting an empty message with subject line uget 0904.0022 or in gzipped form by using subject line get 0904.0022 to: math(a)arXiv.org.

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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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