Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Frank Morgan and Aldo Pratelli
by alspach＠math.okstate.edu 20 Dec '11

20 Dec '11

This is an announcement for the paper "Existence of isoperimetric regions in $\R^n$ with density" by Frank Morgan and Aldo Pratelli. Abstract: We prove the existence of isoperimetric regions in $\R^n$ with density under various hypotheses on the growth of the density. Along the way we prove results on the boundedness of isoperimetric regions. Archive classification: math.FA math.AP Remarks: 31 pages, 4 figures Submitted from: aldo.pratelli(a)unipv.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.5160 or http://arXiv.org/abs/1111.5160

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Abstract of a paper by J. Lopez-Abad and S. Todorcevic
by alspach＠math.okstate.edu 20 Dec '11

20 Dec '11

This is an announcement for the paper "Positional graphs and conditional structure of weakly null sequences" by J. Lopez-Abad and S. Todorcevic. Abstract: We prove that, unless assuming additional set theoretical axioms, there are no reflexive space without unconditional sequences of density the continuum. We give for every integer $n$ there are normalized weakly-null sequences of length $\om_n$ without unconditional subsequences. This together with a result of \cite{Do-Lo-To} shows that $\om_\omega$ is the minimal cardinal $\kappa$ that could possibly have the property that every weakly null $\kappa$-sequence has an infinite unconditional basic subsequence . We also prove that for every cardinal number $\ka$ which is smaller than the first $\om$-Erd\"os cardinal there is a normalized weakly-null sequence without subsymmetric subsequences. Finally, we prove that mixed Tsirelson spaces of uncountable densities must always contain isomorphic copies of either $c_0$ or $\ell_p$, with $p\ge 1$. Archive classification: math.FA math.LO Mathematics Subject Classification: Primary 46B03, 03E35, Secondary 03E02, 03E55, 46B26, 46A35 Submitted from: abad(a)icmat.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.5150 or http://arXiv.org/abs/1111.5150

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Abstract of a paper by Spiros A. Argyros and Kevin Beanland
by alspach＠math.okstate.edu 20 Dec '11

20 Dec '11

This is an announcement for the paper "On spaces admitting no $\ell_p$ or $c_0$ spreading model" by Spiros A. Argyros and Kevin Beanland. Abstract: It is shown that for each separable Banach space $X$ not admitting $\ell_1$ as a spreading model there is a space $Y$ having $X$ as a quotient and not admitting any $\ell_p$ for $1 \leq p < \infty$ or $c_0$ as a spreading model. We also include the solution to a question of W.B. Johnson and H.P. Rosenthal on the existence of a separable space not admitting as a quotient any space with separable dual. Archive classification: math.FA Mathematics Subject Classification: 46B06 Remarks: 17 pages Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.4714 or http://arXiv.org/abs/1111.4714

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Abstract of a paper by Christian Le Merdy
by alspach＠math.okstate.edu 28 Nov '11

28 Nov '11

This is an announcement for the paper "A sharp equivalence between $H^\infty$ functional calculus and square function estimates" by Christian Le Merdy. Abstract: Let T_t = e^{-tA} be a bounded analytic semigroup on Lp, with 1<p<\infty. It is known that if A and its adjoint A^* both satisfy square function estimates \bignorm{\bigl(\int_{0}^{\infty}\vert A^{1/2} T_t(x)\vert^2\, dt\,\bigr)^{1/2}_{Lp} \lesssim \norm{x} and \bignorm{\bigl(\int_{0}^{\infty}\vert A^{*}^{1/2} T_t^*(y)\vert^2\, dt\,\bigr)^{1/2}_{Lp'} \lesssim \norm{y} for x in Lp and y in Lp', then A admits a bounded H^{\infty}(\Sigma_\theta) functional calculus for any \theta>\frac{\pi}{2}. We show that this actually holds true for some \theta<\frac{\pi}{2}. Archive classification: math.FA Mathematics Subject Classification: 47A60, 47D06 Submitted from: clemerdy(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.3719 or http://arXiv.org/abs/1111.3719

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Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
by alspach＠math.okstate.edu 28 Nov '11

28 Nov '11

This is an announcement for the paper "A reflexive HI space with the hereditary Invariant Subspace Property" by Spiros A. Argyros and Pavlos Motakis. Abstract: A reflexive hereditarily indecomposable Banach space $\mathfrak{X}_{_{^\text{ISP}}}$ is presented, such that for every $Y$ infinite dimensional closed subspace of $\mathfrak{X}_{_{^\text{ISP}}}$ and every bounded linear operator $T:Y\rightarrow Y$, the operator $T$ admits a non-trivial closed invariant subspace. Archive classification: math.FA math.OA Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45, 47A15 Remarks: 39 pages, no figures Submitted from: pmotakis(a)central.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.3603 or http://arXiv.org/abs/1111.3603

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Abstract of a paper by Diogo Diniz, Gustavo Munoz-Fernandez, Daniel Pellegrino and Juan B. Seoane-Sepulveda
by alspach＠math.okstate.edu 28 Nov '11

28 Nov '11

This is an announcement for the paper "Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars" by Diogo Diniz, Gustavo Munoz-Fernandez, Daniel Pellegrino and Juan B. Seoane-Sepulveda. Abstract: The Bohnenblust-Hille inequality was obtained in 1931 and (in the case of real scalars) asserts that for every positive integer $N$ and every $m$-linear mapping $T:\ell_{\infty}^{N}\times\cdots\times\ell_{\infty}^{N}\rightarrow \mathbb{R}$ one has \begin{equation*} \left( \sum\limits_{i_{1},...,i_{m}=1}^{N}\left\vert T(e_{i_{^{1}}},...,e_{i_{m}})\right\vert ^{\frac{2m}{m+1}}\right) ^{\frac{m+1}{2m}}\leq C_{m}\left\Vert T\right\Vert , \end{equation*} for some positive constant $C_{m}$. Since then, several authors obtained upper estimates for the values of $C_{m}$. However, the novelty presented in this short note is that we provide lower (and non-trivial) bounds for $C_{m}$. Archive classification: math.FA Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.3253 or http://arXiv.org/abs/1111.3253

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Abstract of a paper by Tal Weissblat
by alspach＠math.okstate.edu 28 Nov '11

28 Nov '11

This is an announcement for the paper "Santalo region of a log-concave function" by Tal Weissblat. Abstract: In this paper we define the Santalo region and the Floating body of a log-concave function. We then study their properties. Our main result is that any relation of Floating body and Santalo region of a convex body is translated to a relation of Floating body and Santalo region of an even log-concave function Archive classification: math.FA Submitted from: talvisbl(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.2409 or http://arXiv.org/abs/1111.2409

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Abstract of a paper by S. K. Mercourakis and G. Vassiliadis
by alspach＠math.okstate.edu 28 Nov '11

28 Nov '11

This is an announcement for the paper "Equilateral sets in infinite dimensional Banach spaces" by S. K. Mercourakis and G. Vassiliadis. Abstract: We show that every Banach space $X$ containing an isomorphic copy of $c_0$ has an infinite equilateral set and also that if $X$ has a bounded biorthogonal system of size $\alpha$ then it can be renormed so as to admit an equilateral set of equal size. If $K$ is any compact non metrizable space, then under a certain combinatorial condition on $K$ the Banach space $C(K)$ has an uncountable equilateral set. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary 46B20, Secondary 46B26, 46B04 Remarks: 15 pages, no figures Submitted from: smercour(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.2273 or http://arXiv.org/abs/1111.2273

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Abstract of a paper by Cedric Arhancet
by alspach＠math.okstate.edu 28 Nov '11

28 Nov '11

This is an announcement for the paper "Unconditionality, Fourier multipliers and Schur multipliers" by Cedric Arhancet. Abstract: Let $G$ be an infinite locally compact abelian group. If $X$ is Banach space, we show that if every bounded Fourier multiplier $T$ on $L^2(G)$ has the property that $T\ot Id_X$ is bounded on $L^2(G,X)$ then the Banach space $X$ is isomorphic to a Hilbert space. Moreover, if $1<p<\infty$, $p\not=2$, we prove that there exists a bounded Fourier multiplier on $L^p(G)$ which is not completely bounded. Finally, we examine unconditionality from the point of view of Schur multipliers. Indeed, we give several sufficient conditions to know if a Banach space or an operator space is isomorphic to a Hilbert space or completely isomorphic to an operator Hilbert space. Archive classification: math.FA math.OA Remarks: 16 pages Submitted from: cedric.arhancet(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.1664 or http://arXiv.org/abs/1111.1664

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Abstract of a paper by Marius Junge and Qiang Zeng
by alspach＠math.okstate.edu 28 Nov '11

28 Nov '11

This is an announcement for the paper "Noncommutative Bennett and Rosenthal Inequalities" by Marius Junge and Qiang Zeng. Abstract: In this paper we extend Bennett's and Bernstein's inequality to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis, and Pinelis, Utev for commutative random variables. We also present new best constants in Rosenthal's inequality. Applying these results to random Fourier projections, we recover and elaborate on fundamental results from compressed sensing, due to Candes, Romberg, and Tao. Archive classification: math.PR math.FA math.OA Mathematics Subject Classification: 46L53, 46L50, 60E15, 60F10, 94A12 Remarks: 28 pages Submitted from: zeng8(a)illinois.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.1027 or http://arXiv.org/abs/1111.1027

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