- Banach - mathdept.okstate.edu

Abstract of a paper by C. Ruiz, J. Lopez-Abad and P. Tradacete
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "The convex hull of a Banach-Saks set" by C. Ruiz, J. Lopez-Abad and P. Tradacete. Abstract: A subset $A$ of a Banach space is called Banach-Saks when every sequence in $A$ has a Ces{\`a}ro convergent subsequence. Our interest here focusses on the following problem: is the convex hull of a Banach-Saks set again Banach-Saks? By means of a combinatorial argument, we show that in general the answer is negative. However, sufficient conditions are given in order to obtain a positive result. Archive classification: math.FA math.CO math.LO Mathematics Subject Classification: 46B50, 05D10 Remarks: 29 pages Submitted from: abad(a)icmat.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4851 or http://arXiv.org/abs/1209.4851

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Abstract of a paper by D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "Unconditional structures of translates for $L_p(R^d)$" by D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak. Abstract: We prove that a sequence $(f_i)_{i=1}^\infty$ of translates of a fixed $f\in L_p(R)$ cannot be an unconditional basis of $L_p(R)$ for any $1\le p<\infty$. In contrast to this, for every $2<p<\infty$, $d\in N$ and unbounded sequence $(\lambda_n)_{n\in N}\subset R^d$ we establish the existence of a function $f\in L_p(R^d)$ and sequence $(g^*_n)_{n\in N}\subset L_p^*(R^d)$ such that $(T_{\lambda_n} f, g^*_n)_{n\in N}$ forms an unconditional Schauder frame for $L_p(R^d)$. In particular, there exists a Schauder frame of integer translates for $L_p(R)$ if (and only if) $2<p<\infty$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 54H05, 42C15 Remarks: 22 pages Submitted from: dfreema7(a)slu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4619 or http://arXiv.org/abs/1209.4619

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Abstract of a paper by Tomasz Kochanek and Michal Lewicki
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "Characterisation of $L_p$-norms via H\"older's inequality" by Tomasz Kochanek and Michal Lewicki. Abstract: We characterise $L_p$-norms on the space of integrable step functions, defined on a probabilistic space, via H\"older's type inequality with an optimality condition. Archive classification: math.FA Mathematics Subject Classification: 26D15, 39B05, 46B04 Submitted from: t_kochanek(a)wp.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4587 or http://arXiv.org/abs/1209.4587

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Abstract of a paper by D. Pellegrino and J.B. Seoane-Sepulveda
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "The Bohnenblust-Hille inequality for real homogeneous polynomials is hypercontractive and this result is optimal" by D. Pellegrino and J.B. Seoane-Sepulveda. Abstract: It was recently shown by A. Montanaro that the low growth of the constants of the multilinear Bohnenblust-Hille inequality, for real scalars, plays a crucial role in Quantum Information Theory. In this paper, among other results, we show that the polynomial Bohnenblust--Hille inequality, for real scalars, is hypercontractive; the case of complex scalars was recently proved in the paper "The Bohnhenblust-Hille inequality for homogeneous polynomials is hypercontractive" , by Defant, Frerick, Ortega-Cerd\'{a}, Ouna\"{\i}es, and Seip (Annals of Mathematics, 2011). Our proof is presented in a simple form, by making use of a deep result that dates back to Erd\"os (Bull. Amer. Math. Soc., 1947). We also show, in strong contrast to what happens in the case of multilinear mappings, that the hypercontractive growth of these constants cannot be improved. The complex version of this result remains still open. Archive classification: math.FA Mathematics Subject Classification: 46G25, 30B50 Submitted from: jseoane(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4632 or http://arXiv.org/abs/1209.4632

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Abstract of a paper by Almut Burchard and Gregory R. Chambers
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "Perimeter under multiple Steiner symmetrizations" by Almut Burchard and Gregory R. Chambers. Abstract: Steiner symmetrization along n linearly independent directions transforms every compact subset of R^n into a set of finite perimeter. Archive classification: math.MG math.FA Mathematics Subject Classification: 28A75 (26B15, 52A38) Remarks: 12 pages, 1 figure Submitted from: almut(a)math.toronto.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4521 or http://arXiv.org/abs/1209.4521

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Abstract of a paper by Piotr Koszmider
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "Universal objects and associations between classes of Banach spaces classes of compact spaces" by Piotr Koszmider. Abstract: In the context of classical associations between classes of Banach spaces and classes of compact Hausdorff spaces we survey known results and open questions concerning the existence and nonexistence of universal Banach spaces and of universal compact spaces in various classes. This gives quite a complex network of interrelations which quite often depend on additional set-theoretic assumptions. Archive classification: math.FA math.GN math.LO Submitted from: piotr.math(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4294 or http://arXiv.org/abs/1209.4294

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Abstract of a paper by David Alonso-Gutierrez and Jesus Bastero
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "The variance conjecture on some polytopes" by David Alonso-Gutierrez and Jesus Bastero. Abstract: We show that any random vector uniformly distributed on any hyperplane projection of $B_1^n$ or $B_\infty^n$ verifies the variance conjecture $$\text{Var }|X|^2\leq C\sup_{\xi\in S^{n-1}}\E\langle X,\xi\rangle^2\E|X|^2.$$ Furthermore, a random vector uniformly distributed on a hyperplane projection of $B_\infty^n$ verifies a negative square correlation property and consequently any of its linear images verifies the variance conjecture. Archive classification: math.FA Submitted from: bastero(a)unizar.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4270 or http://arXiv.org/abs/1209.4270

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Abstract of a paper by Paul F. X. Mueller
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "A decomposition for Hardy martingales. Part II" by Paul F. X. Mueller. Abstract: We prove Davis and Garsia Inequalities for dyadic perturbations of Hardy Martingales. We apply those to estimate the $L^1 $ distance of a dyadic martingale to the class of Hardy martingales. We revisit Bourgains embedding of $L^1$ into the quotient space $ L^1 / H^1 . $ Archive classification: math.FA math.CV Submitted from: pfxm(a)bayou.uni-linz.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.3964 or http://arXiv.org/abs/1209.3964

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Abstract of a paper by Antonio Aviles and Stevo Todorcevic
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "Analytic multiple gaps" by Antonio Aviles and Stevo Todorcevic. Abstract: We prove that there is a finite basis for analytic n-gaps, and we prove a number of results concerning the structure of an analytic n-gap when restricted to an infinite subset. This has applications in the study of how different classes of subsequences are mixed inside a sequence of vectors in a Banach space Archive classification: math.LO math.CO math.FA Mathematics Subject Classification: Primary 03E15, 28A05, 05D10, Secondary 46B15 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.3751 or http://arXiv.org/abs/1209.3751

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Abstract of a paper by Eleonora Cinti and Aldo Pratelli
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "The $\epsilon-\epsilon^\beta$ property, the boundedness of isoperimetric sets in $\R^N$ with density, and some applications" by Eleonora Cinti and Aldo Pratelli. Abstract: We show that every isoperimetric set in R^N with density is bounded if the density is continuous and bounded by above and below. This improves the previously known boundedness results, which basically needed a Lipschitz assumption; on the other hand, the present assumption is sharp, as we show with an explicit example. To obtain our result, we observe that the main tool which is often used, namely a classical ``\epsilon-\epsilon'' property already discussed by Allard, Almgren and Bombieri, admits a weaker counterpart which is still sufficient for the boundedness, namely, an ``\epsilon-\epsilon^\beta'' version of the property. And in turn, while for the validity of the first property the Lipschitz assumption is essential, for the latter the sole continuity is enough. We conclude by deriving some consequences of our result about the existence and regularity of isoperimetric sets. Archive classification: math.FA Submitted from: eleonora.cinti(a)unipv.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.3624 or http://arXiv.org/abs/1209.3624

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