June 2013 - Banach - mathdept.okstate.edu

Abstract of a paper by Jamilson Ramos Campos
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "An abstract result on Cohen strongly summing operators" by Jamilson Ramos Campos. Abstract: We present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of Cohen strongly summing linear operators. Our argument is extended to multilinear operators and, as a consequence, we establish a few alternative characterizations for the class of Cohen strongly summing multilinear operators. Archive classification: math.FA Remarks: 9 pages Submitted from: jamilson(a)dce.ufpb.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.7276 or http://arXiv.org/abs/1305.7276

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Abstract of a paper by D. Freeman, E. Odell, B. Sari, and Th. Schlumprecht
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Equilateral sets in uniformly smooth Banach spaces" by D. Freeman, E. Odell, B. Sari, and Th. Schlumprecht. Abstract: Let $X$ be an infinite dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exists a constant $\lambda>0$ and an infinite sequence $(x_i)_{i=1}^\infty\subset X$ such that $\|x_i-x_j\|=\lambda$ for all $i\neq j$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B04 Remarks: 11 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/1305.6750 or http://arXiv.org/abs/1305.6750

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Abstract of a paper by Richard Aron, Yun Sung Choi, Sun Kwang Kim, Han Ju Lee, and Miguel Martin
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "The Bishop-Phelps-Bollob\'as version of Lindenstrauss properties A" by Richard Aron, Yun Sung Choi, Sun Kwang Kim, Han Ju Lee, and Miguel Martin. Abstract: We study a Bishop-Phelps-Bollob\'as version of Lindenstrauss properties A and B. For domain spaces, we study Banach spaces $X$ such that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property (BPBp) for every Banach space $Y$. We show that in this case, there exists a universal function $\eta_X(\eps)$ such that for every $Y$, the pair $(X,Y)$ has the BPBp with this function. This allows us to prove some necessary isometric conditions for $X$ to have the property. We also prove that if $X$ has this property in every equivalent norm, then $X$ is one-dimensional. For range spaces, we study Banach spaces $Y$ such that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property for every Banach space $X$. In this case, we show that there is a universal function $\eta_Y(\eps)$ such that for every $X$, the pair $(X,Y)$ has the BPBp with this function. This implies that this property of $Y$ is strictly stronger than Lindenstrauss property B. The main tool to get these results is the study of the Bishop-Phelps-Bollob\'as property for $c_0$-, $\ell_1$- and $\ell_\infty$-sums of Banach spaces. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.6420 or http://arXiv.org/abs/1305.6420

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Abstract of a paper by Tomasz Kobos
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Equilateral dimension of some classes of normed spaces" by Tomasz Kobos. Abstract: An equilateral dimension of a normed space is a maximal number of pairwise equidistant points of this space. The aim of this paper is to study the equilateral dimension of certain classes of finite dimensional normed spaces. The well-known conjecture states that the equilateral dimension of any $n$-dimensional normed space is not less than $n+1$. By using an elementary continuity argument, we establish it in the following classes of spaces: permutation-invariant spaces, Orlicz-Musielak spaces and in one codimensional subspaces of $\ell^n_{\infty}$. For smooth and symmetric spaces, Orlicz-Musielak spaces satisfying an additional condition and every $(n-1)$-dimensional subspace of $\ell^{n}_{\infty}$ we also provide some weaker bounds on the equilateral dimension for every space which is sufficiently close to one of these. This generalizes the result of Swanepoel and Villa concerning the $\ell_p^n$ spaces. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B85, 46B20, 52C17, 52A15, 52A20 Remarks: 12 pages Submitted from: tkobos(a)wp.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.6288 or http://arXiv.org/abs/1305.6288

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Abstract of a paper by Jameson Cahill, Peter G. Casazza, Jesse Peterson and Lindsey
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Real phase retrieval by projections" by Jameson Cahill, Peter G. Casazza, Jesse Peterson and Lindsey. Abstract: The problem of recovering a vector from the absolute values of its inner products against a family of measurement vectors has been well studied in mathematics and engineering. A generalization of this phase retrieval problem also exists in engineering: recovering a vector from measurements consisting of norms of its orthogonal projections onto a family of subspaces. There exist semidefinite programming algorithms to solve this problem, but much remains unknown for this more general case. Can families of subspaces for which such measurements are injective be completely classified? What is the minimal number of subspaces required to have injectivity? How closely does this problem compare to the usual phase retrieval problem with families of measurement vectors? In this paper, we answer or make incremental steps toward these questions. We provide several characterizations of subspaces which yield injective measurements, and through a concrete construction, we prove the surprising result that phase retrieval can be achieved with $2M-1$ projections of arbitrary rank in $\HH_M$. Finally we present several open problems as we discuss issues unique to the phase retrieval problem with subspaces. Archive classification: math.FA Submitted from: lmwvh4(a)mail.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.6226 or http://arXiv.org/abs/1305.6226

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Abstract of a paper by Jan van Neerven
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Compactness in the Lebesgue-Bochner spaces L^p(\mu;X)" by Jan van Neerven. Abstract: Let (\Omega,\mu) be a finite measure space, X a Banach space, and let 1\le p<\infty. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of L^p(\mu;X) is relatively compact if and only if it is uniformly p-integrable, uniformly tight, and scalarly relatively compact. Archive classification: math.FA Mathematics Subject Classification: Primary: 46E40, Secondary: 46E30, 46B50 Remarks: 5 pages, submitted for publication Submitted from: J.M.A.M.vanNeerven(a)tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.5688 or http://arXiv.org/abs/1305.5688

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Abstract of a paper by Diana Marcela Serrano-Rodriguez
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Absolutely \gamma-summing multilinear operators" by Diana Marcela Serrano-Rodriguez. Abstract: In this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators. We show that several previous results on different contexts (absolutely summing, almost summing, Cohen summing) are particular cases of our general results. Archive classification: math.FA Submitted from: dmserrano0(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.4626 or http://arXiv.org/abs/1305.4626

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Abstract of a paper by Costas Poulios and Athanasios Tsarpalias
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Some combinatorial principles for trees and applications to tree-families in Banach spaces" by Costas Poulios and Athanasios Tsarpalias. Abstract: Suppose that $(x_s)_{s\in S}$ is a normalized family in a Banach space indexed by the dyadic tree $S$. Using Stern's combinatorial theorem we extend important results from sequences in Banach spaces to tree-families. More precisely, assuming that for any infinite chain $\beta$ of $S$ the sequence $(x_s)_{s\in\beta}$ is weakly null, we prove that there exists a subtree $T$ of $S$ such that for any infinite chain $\beta$ of $T$ the sequence $(x_s)_{s\in\beta}$ is nearly (resp., convexly) unconditional. In the case where $(f_s)_{s\in S}$ is a family of continuous functions, under some additional assumptions, we prove the existence of a subtree $T$ of $S$ such that for any infinite chain $\beta$ of $T$, the sequence $(f_s)_{s\in\beta}$ is unconditional. Finally, in the more general setting where for any chain $\beta$, $(x_s)_{s\in\beta}$ is a Schauder basic sequence, we obtain a dichotomy result concerning the semi-boundedly completeness of the sequences $(x_s)_{s\in\beta}$. Archive classification: math.FA Mathematics Subject Classification: 05D10, 46B15 Submitted from: k-poulios(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.4186 or http://arXiv.org/abs/1305.4186

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Abstract of a paper by Michael Dymond and Olga Maleva
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Differentiability inside sets with upper Minkowski dimension one" by Michael Dymond and Olga Maleva. Abstract: We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets $S$ of upper Minkowski dimension one such that every Lipschitz function defined on the whole space is differentiable inside $S$. Such sets are constructed explicitly. Archive classification: math.FA Mathematics Subject Classification: 46T20 Remarks: 23 pages Submitted from: o.maleva(a)bham.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.3154 or http://arXiv.org/abs/1305.3154

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Abstract of a paper by Yousef estaremi
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "multiplication conditional expectation type operators on Orlicz" by Yousef estaremi. Abstract: In this paper we consider a generalized conditional-type Holder- inequality and investigate some classic properties of multiplication conditional expectation type operators on Orlicz-spaces. Archive classification: math.FA Remarks: 12 pages Submitted from: estaremi(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.2481 or http://arXiv.org/abs/1305.2481

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