- Banach - mathdept.okstate.edu

Abstract of a paper by Shahar Mendelson
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "A remark on the diameter of random sections of convex bodies" by Shahar Mendelson. Abstract: We obtain a new upper estimate on the Euclidean diameter of the intersection of the kernel of a random matrix with iid rows with a given convex body. The proof is based on a small-ball argument rather than on concentration and thus the estimate holds for relatively general matrix ensembles. Archive classification: math.FA Submitted from: shahar.mendelson(a)anu.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.3608 or http://arXiv.org/abs/1312.3608

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Abstract of a paper by Dongyang Chen, Lei Li and Bentuo Zheng
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Perturbations of frames" by Dongyang Chen, Lei Li and Bentuo Zheng. Abstract: In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic. Archive classification: math.FA Remarks: to appear in Acta MAth. Sinica, English Series Submitted from: leilee(a)nankai.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.3460 or http://arXiv.org/abs/1312.3460

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Abstract of a paper by R. Lechner and M. Passenbrunner
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Adaptive deterministic dyadic grids on spaces of homogeneous type" by R. Lechner and M. Passenbrunner. Abstract: In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector--valued operators rearranging martingale difference sequences such as the Haar system. Archive classification: math.FA Mathematics Subject Classification: 46E40 Remarks: 18 pages, 2 figures Submitted from: lechner(a)bayou.uni-linz.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.3490 or http://arXiv.org/abs/1312.3490

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Abstract of a paper by Elizabeth S. Meckes and Mark W. Meckes
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "On the equivalence of modes of convergence for log-concave measures" by Elizabeth S. Meckes and Mark W. Meckes. Abstract: An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note, we explore the extent to which different notions of distance between probability measures are comparable for log-concave distributions. Our results imply that weak convergence of isotropic log-concave distributions is equivalent to convergence in total variation, and is further equivalent to convergence in relative entropy when the limit measure is Gaussian. Archive classification: math.PR math.FA Submitted from: mark.meckes(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.3094 or http://arXiv.org/abs/1312.3094

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Abstract of a paper by Eytyhios Glakousakis and Sophocles Mercourakis
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "On the existence of 1-separated sequences on the unit ball of a finite dimensional Banach space" by Eytyhios Glakousakis and Sophocles Mercourakis. Abstract: Given a finite dimensional Banach space X with dimX = n and an Auerbach basis of X, it is proved that: there exists a set D of n + 1 linear combinations (with coordinates 0, -1, +1) of the members of the basis, so that each pair of different elements of D have distance greater than one. Archive classification: math.FA math.CO math.MG 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/1312.2896 or http://arXiv.org/abs/1312.2896

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Abstract of a paper by N. Machrafi, A. Elbour, and M. Moussa
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Some characterizations of almost limited sets and applications" by N. Machrafi, A. Elbour, and M. Moussa. Abstract: Recently, J.X. Chen et al. introduced and studied the class of almost limited sets in Banach lattices. In this paper we establish some characterizations of almost limited sets in Banach lattices (resp. wDP* property of Banach lattices), that generalize some results obtained by J.X. Chen et al.. Also, we introduce and study the class of the almost limited operators, which maps the closed unit bull of a Banach space to an almost limited subset of a Banach lattice. Some results about the relationship between the class of almost limited operators and that of L-weakly compact (resp. M-weakly compact, resp. compact) operators are presented. Archive classification: math.FA Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65 (Secondary) Remarks: 9 pages Submitted from: azizelbour(a)hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.2770 or http://arXiv.org/abs/1312.2770

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Abstract of a paper by Oleg Reinov
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "On operators with bounded approximation property" by Oleg Reinov. Abstract: It is known that any separable Banach space with BAP is a complemented subspace of a Banach space with a basis. We show that every operator with bounded approximation property, acting from a separable Banach space, can be factored through a Banach space with a basis. Archive classification: math.FA Mathematics Subject Classification: 46B28 Remarks: 5 pages Submitted from: orein51(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.2116 or http://arXiv.org/abs/1312.2116

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Abstract of a paper by Daniel Carando, Daniel Galicer and Damian Pinasco
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Energy integrals and metric embedding theory" by Daniel Carando, Daniel Galicer and Damian Pinasco. Abstract: For some centrally symmetric convex bodies $K\subset \mathbb R^n$, we study the energy integral $$ \sup \int_{K} \int_{K} \|x - y\|_r^{p}\, d\mu(x) d\mu(y), $$ where the supremum runs over all finite signed Borel measures $\mu$ on $K$ of total mass one. In the case where $K = B_q^n$, the unit ball of $\ell_q^n$ (for $1 \leq q \leq 2$) or an ellipsoid, we obtain the exact value or the correct asymptotical behavior of the supremum of these integrals. We apply these results to a classical embedding problem in metric geometry. We consider in $\mathbb R^n$ the Euclidean distance $d_2$. For $0 < \alpha < 1$, we estimate the minimum $R$ for which the snowflaked metric space $(K, d_2^{\alpha})$ may be isometrically embedded on the surface of a Hilbert sphere of radius $R$. Archive classification: math.MG math.FA Mathematics Subject Classification: 51M16, 52A23, 31C45, 51K05, 54E40 Remarks: 18 pages Submitted from: dgalicer(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.0678 or http://arXiv.org/abs/1312.0678

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Abstract of a paper by Michael Kelly
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "The Blaschke-Santalo Inequality" by Michael Kelly. Abstract: The Blaschke-Santalo inequality is the assertion that the volume product of a symmetric convex body in Euclidean space is maximized by the Euclidean unit ball. In this paper we give a Fourier analytic proof of this fact. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A40 (Primary), 42A05, 42A85, 52A39, 46E22 (Secondary) Remarks: 11 pages, 4 figures Submitted from: mkelly(a)math.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.0244 or http://arXiv.org/abs/1312.0244

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Abstract of a paper by Manaf Adnan Salah
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Lipschitz $\left(\mathfrak{m}^L\left(s;q\right),p\right)$ and $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing maps" by Manaf Adnan Salah. Abstract: Building upon the linear version of mixed summable sequences in arbitrary Banach spaces of A. Pietsch, we introduce a nonlinear version of his concept and study its properties. Extending previous work of J. D. Farmer, W. B. Johnson and J. A. Ch\'avez-Dom\'inguez, we define Lipschitz $\left(\mathfrak{m}^L\left(s;q\right),p\right)$ and Lipschitz $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing maps and establish inclusion theorems, composition theorems and several characterizations. Furthermore, we prove that the classes of Lipschitz $\left(r,\mathfrak{m}^L\left(r;r\right)\right)-$summing maps with $0<r<1$ coincide. We obtain that every Lipschitz map is Lipschitz $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing map with $1\leq s< p$ and $0<q\leq s$ and discuss a sufficient condition for a Lipschitz composition formula as in the linear case of A. Pietsch. Moreover, we discuss a counterexample of the nonlinear composition formula, thus solving a problem by J. D. Farmer and W. B. Johnson. Archive classification: math.FA Mathematics Subject Classification: 47L20 47B10 Submitted from: manaf-adnan.salah(a)uni-jena.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.7575 or http://arXiv.org/abs/1311.7575

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