Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Anthony Weston
by alspach＠fourier.math.okstate.edu 23 Jul '08

23 Jul '08

This is an announcement for the paper "Optimal lower bounds on the maximal p-negative type of finite metric spaces" by Anthony Weston. Abstract: This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric space. Examples show that these lower bounds can easily be best possible under clearly delineated circumstances. We further point out that the entire theory holds (more generally) for finite semi-metric spaces without modification and wherein the lower bounds are always optimal. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20 Remarks: 10 pages The source file(s), Gap.tex: 36066 bytes, is(are) stored in gzipped form as 0807.2705.gz with size 11kb. The corresponding postcript file has gzipped size 95kb. Submitted from: westona(a)canisius.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2705 or http://arXiv.org/abs/0807.2705 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2705 or in gzipped form by using subject line get 0807.2705 to: math(a)arXiv.org.

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Abstract of a paper by Spiros A. Argyros, Alexander D. Arvanitakis, and Andreas G. Tolias
by alspach＠fourier.math.okstate.edu 17 Jul '08

17 Jul '08

This is an announcement for the paper "Saturated extensions, the attractors method and Hereditarily James Tree Space" by Spiros A. Argyros, Alexander D. Arvanitakis, and Andreas G. Tolias. Abstract: In the present work we provide a variety of examples of HI Banach spaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors. Archive classification: math.FA The source file(s), Aat6.tex: 290045 bytes, is(are) stored in gzipped form as 0807.2392.gz with size 77kb. The corresponding postcript file has gzipped size 377kb. 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/0807.2392 or http://arXiv.org/abs/0807.2392 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2392 or in gzipped form by using subject line get 0807.2392 to: math(a)arXiv.org.

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Abstract of a paper by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias
by alspach＠fourier.math.okstate.edu 17 Jul '08

17 Jul '08

This is an announcement for the paper "Strictly singular non-compact diagonal operators on HI spaces" by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias. Abstract: We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with respect to the basis \seq{e}{n} contains an isomorphic copy of $\ell_{\infty}(\N)$. \end{abstract} Archive classification: math.FA Mathematics Subject Classification: 46B28, 46B20, 46B03 The source file(s), diagonal_adt_1.tex: 147103 bytes, is(are) stored in gzipped form as 0807.2388.gz with size 39kb. The corresponding postcript file has gzipped size 213kb. 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/0807.2388 or http://arXiv.org/abs/0807.2388 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2388 or in gzipped form by using subject line get 0807.2388 to: math(a)arXiv.org.

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Abstract of a paper by Christian Rosendal
by alspach＠fourier.math.okstate.edu 17 Jul '08

17 Jul '08

This is an announcement for the paper "An exact Ramsey principle for block sequences" by Christian Rosendal. Abstract: We prove an exact, i.e., formulated without $\Delta$-expansions, Ramsey principle for infinite block sequences in vector spaces over countable fields, where the two sides of the dichotomic principle are represented by respectively winning strategies in Gowers' block sequence game and winning strategies in the infinite asymptotic game. This allows us to recover Gowers' dichotomy theorem for block sequences in normed vector spaces by a simple application of the basic determinacy theorem for infinite asymptotic games. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B03, 03E15 The source file(s), ExactRamseyPrinciples17submitted.tex: 37130 bytes, is(are) stored in gzipped form as 0807.2205.gz with size 11kb. The corresponding postcript file has gzipped size 82kb. Submitted from: rosendal(a)math.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2205 or http://arXiv.org/abs/0807.2205 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2205 or in gzipped form by using subject line get 0807.2205 to: math(a)arXiv.org.

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Abstract of a paper by William B. Johnson and Assaf Naor
by alspach＠fourier.math.okstate.edu 17 Jul '08

17 Jul '08

This is an announcement for the paper "The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite" by William B. Johnson and Assaf Naor. Abstract: Let $X$ be a normed space that satisfies the Johnson-Lindenstrauss lemma (J-L lemma, in short) in the sense that for any integer $n$ and any $x_1,\ldots,x_n\in X$ there exists a linear mapping $L:X\to F$, where $F\subseteq X$ is a linear subspace of dimension $O(\log n)$, such that $\|x_i-x_j\|\le\|L(x_i)-L(x_j)\|\le O(1)\cdot\|x_i-x_j\|$ for all $i,j\in \{1,\ldots, n\}$. We show that this implies that $X$ is almost Euclidean in the following sense: Every $n$-dimensional subspace of $X$ embeds into Hilbert space with distortion $2^{2^{O(\log^*n)}}$. On the other hand, we show that there exists a normed space $Y$ which satisfies the J-L lemma, but for every $n$ there exists an $n$-dimensional subspace $E_n\subseteq Y$ whose Euclidean distortion is at least $2^{\Omega(\alpha(n))}$, where $\alpha$ is the inverse Ackermann function. Archive classification: math.FA math.MG The source file(s), JL-L3.1.TEX: 43297 bytes, is(are) stored in gzipped form as 0807.1919.gz with size 14kb. The corresponding postcript file has gzipped size 74kb. Submitted from: naor(a)cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.1919 or http://arXiv.org/abs/0807.1919 or by email in unzipped form by transmitting an empty message with subject line uget 0807.1919 or in gzipped form by using subject line get 0807.1919 to: math(a)arXiv.org.

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Abstract of a paper by Marisa Zymonopoulou
by alspach＠fourier.math.okstate.edu 10 Jul '08

10 Jul '08

This is an announcement for the paper "The complex Busemann-Petty problem for arbitrary measures" by Marisa Zymonopoulou. Abstract: The complex Busemann-Petty problem asks whether origin symmetric convex bodies in C^n with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n\leq 3 and negative if n\geq 4. In this article we show that the answer remains the same if the volume is replaced by an "almost" arbitrary measure. This result is the complex analogue of Zvavitch's generalization to arbitrary measures of the original real Busemann-Petty problem. Archive classification: math.FA The source file(s), CBPGM.tex: 37275 bytes, is(are) stored in gzipped form as 0807.0779.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: marisa(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.0779 or http://arXiv.org/abs/0807.0779 or by email in unzipped form by transmitting an empty message with subject line uget 0807.0779 or in gzipped form by using subject line get 0807.0779 to: math(a)arXiv.org.

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Abstract of a paper by Marisa Zymonopoulou
by alspach＠fourier.math.okstate.edu 10 Jul '08

10 Jul '08

This is an announcement for the paper "The modified complex Busemann-Petty problem on sections of convex bodies" by Marisa Zymonopoulou. Abstract: Since the answer to the complex Busemann-Petty problem is negative in most dimensions, it is natural to ask what conditions on the (n-1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative answer in all dimensions. Archive classification: math.FA The source file(s), MCBP.tex: 44421 bytes, is(are) stored in gzipped form as 0807.0776.gz with size 12kb. The corresponding postcript file has gzipped size 104kb. Submitted from: marisa(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.0776 or http://arXiv.org/abs/0807.0776 or by email in unzipped form by transmitting an empty message with subject line uget 0807.0776 or in gzipped form by using subject line get 0807.0776 to: math(a)arXiv.org.

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Abstract of a paper by Greg Kuperberg
by alspach＠fourier.math.okstate.edu 10 Jul '08

10 Jul '08

This is an announcement for the paper "From the Mahler conjecture to Gauss linking integrals" by Greg Kuperberg. Abstract: We establish a version of the bottleneck conjecture, which in turn implies a partial solution to the Mahler conjecture on the product $v(K) = (\Vol K)(\Vol K^\circ)$ of the volume of a symmetric convex body $K \in \R^n$ and its polar body $K^\circ$. The Mahler conjecture asserts that the Mahler volume $v(K)$ is minimized (non-uniquely) when $K$ is an $n$-cube. The bottleneck conjecture (in its least general form) asserts that the volume of a certain domain $K^\diamond \subseteq K \times K^\circ$ is minimized when $K$ is an ellipsoid. It implies the Mahler conjecture up to a factor of $(\pi/4)^n \gamma_n$, where $\gamma_n$ is a monotonic factor that begins at $4/\pi$ and converges to $\sqrt{2}$. This strengthens a result of Bourgain and Milman, who showed that there is a constant $c$ such that the Mahler conjecture is true up to a factor of $c^n$. The proof uses a version of the Gauss linking integral to obtain a constant lower bound on $\Vol K^\diamond$, with equality when $K$ is an ellipsoid. It applies to a more general conjecture concerning the join of any two necks of the pseudospheres of an indefinite inner product space. Because the calculations are similar, we will also analyze traditional Gauss linking integrals in the sphere $S^{n-1}$ and in hyperbolic space $H^{n-1}$. Archive classification: math.MG math.DG math.FA Remarks: 10 pages, 4 figures. Dedicated to my father, on no particular The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math/0610904 or http://arXiv.org/abs/math/0610904 or by email in unzipped form by transmitting an empty message with subject line uget math/0610904 or in gzipped form by using subject line get math/0610904 to: math(a)arXiv.org.

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SUMIRFAS-2nd announcement
by Bill Johnson 10 Jul '08

10 Jul '08

2nd ANNOUNCEMENT OF SUMIRFAS 2008 The Informal Regional Functional Analysis Seminar August 8 - 10 Texas A&M University, College Station Confirmed speakers and titles are given below. The schedule for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.tamu.edu/map/building/overview/BLOC.html. Coffee and refreshments will be available in Blocker 155. Julien Giol <giol(a)math.tamu.edu>, David Kerr (chair) <kerr(a)math.tamu.edu>, and Andrew Toms <atoms(a)mathstat.yorku.ca> are organizing a Concentration Week on "Operator Algebras, Dynamics, and Classification" which will take place August 4-8. For more information, go to http://www.math.tamu.edu/~kerr/concweek08.html. Ron Douglas <rdouglas(a)math.tamu.edu> and Jaydeb Sarkar <jsarkar(a)math.tamu.edu> are organizing a Concentration Week on "Multivariate Operator Theory" that will take place July 28 - August 1. For more information, please visit URL http://www.math.tamu.edu/~jsarkar/cowmot.html. On Saturday evening there will be a BBQ at the home of Jan and Bill Johnson. We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cara to book your room, please tell them if you are requesting support. Minorities, women, graduate students, and young researchers are especially encouraged to apply. For logistical 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. Speakers include: Bill Arveson, Maximal vectors in Hilbert space and quantum entanglement Nate Brown, Hilbert modules and the Cuntz semigroup Marius Dadarlat, Finite dimensional approximations of amenable groups Ron DeVore, A Taste of Compressed Sensing Detelin Dosev, Commutators on certain Banach spaces Constanze Liaw, Singular integrals and rank one perturbations Timur Oikhberg, The complexity of the complete isomorphism relation between subspaces of an operator space (joint work with C. Rosendal) Grigoris Paouris, Small ball probability estimates for log-concave measures Chris Phillips, Freeness of actions of finite groups on C*-algebras Bunyamin Sari, On uniform classification of the direct sums of $\ell_p$-spaces Nicole Tomczak-Jaegermann, Random embeddings and other high-dimensional geometric phenomena Elisabeth Werner, Orlicz functions and minima and maxima of random variables

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Abstract of a paper by Konrad J. Swanepoel
by alspach＠fourier.math.okstate.edu 01 Jul '08

01 Jul '08

This is an announcement for the paper "Simultaneous packing and covering in sequence spaces" by Konrad J. Swanepoel. Abstract: We adapt a construction of Klee (1981) to find a packing of unit balls in $\ell_p$ ($1\leq p<\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value $2^{1-1/p}$ is optimal. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20 (primary), 52C17 (secondary) Remarks: 5 pages The source file(s), klee.tex: 14156 bytes, is(are) stored in gzipped form as 0806.4473.gz with size 5kb. The corresponding postcript file has gzipped size 92kb. Submitted from: konrad.swanepoel(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.4473 or http://arXiv.org/abs/0806.4473 or by email in unzipped form by transmitting an empty message with subject line uget 0806.4473 or in gzipped form by using subject line get 0806.4473 to: math(a)arXiv.org.

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