Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Jose Orihuela, Richard J. Smith, and Stanimir Troyanski
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "Strictly convex norms and topology" by Jose Orihuela, Richard J. Smith, and Stanimir Troyanski. Abstract: We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with $G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise those Banach spaces which admit equivalent strictly convex norms, and give an internal topological characterisation of those scattered compact spaces $K$, for which the dual Banach space $C(K)^*$ admits an equivalent strictly convex dual norm. We establish some relationships between (*) and other topological concepts, and the position of several well-known examples in this context. For instance, we show that $C(\mathcal{K})^*$ admits an equivalent strictly convex dual norm, where $\mathcal{K}$ is Kunen's compact space. Also, under the continuum hypothesis CH, we give an example of a compact scattered non-Gruenhage space having (*). Archive classification: math.FA math.GN Submitted from: richard.smith(a)ucd.ie The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5595 or http://arXiv.org/abs/1012.5595

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Abstract of a paper by Antonio Aviles
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "Radon-Nikodym compact spaces of low weight and Banach spaces" by Antonio Aviles. Abstract: We prove that a continuous image of a Radon-Nikod\'{y}m compact space of weight less than b is Radon-Nikod\'{y}m compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated which has density character exactly b. Archive classification: math.FA math.GN Mathematics Subject Classification: Primary 46B26, Secondary 46B22, 46B50, 54G99 Citation: Studia Math. 166 (2005), no. 1, 71–82 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5512 or http://arXiv.org/abs/1012.5512

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Abstract of a paper by Antonio Aviles and Christina Brech
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "A Boolean algebra and a Banach space obtained by push-out iteration" by Antonio Aviles and Christina Brech. Abstract: Under the assumption that the continuum c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(N)/fin has under CH and in the aleph2-Cohen model. We prove a similar result in the category of Banach spaces. Archive classification: math.LO math.CT math.FA Mathematics Subject Classification: 06E05, 03E35, 03G05, 46B26, 54G05, 18A30 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.5051 or http://arXiv.org/abs/1012.5051

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Abstract of a paper by Rodrigo Banuelos and Burgess Davis
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "Donald Burkholder's work in martingales and analysis" by Rodrigo Banuelos and Burgess Davis. Abstract: Overview of Burkholder's work on martingales and analysis Archive classification: math.PR math.FA Submitted from: banuelos(a)math.purdue.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.4849 or http://arXiv.org/abs/1012.4849

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Abstract of a paper by Rodrigo Banuelos
by alspach＠math.okstate.edu 30 Dec '10

30 Dec '10

This is an announcement for the paper "The foundational inequalities of D.L. Burkholder and some of their ramifications" by Rodrigo Banuelos. Abstract: This paper present an overview of some of the applications of the martingale transform inequalities of D.L.~Burkholder to $L^p$-bounds for singular integrals concentrating on $L^p$-bounds for the Hilbert, Riesz, Beurling-Ahlfors transforms and other multipliers obtained by projections (conditional expectations) of transformations of stochastic integrals. The aim is to obtain optimal, or near optimal, bounds in these inequalities. Connections to other areas of mathematics where these inequalities and the techniques to prove them have become of considerable interest in recent years, are also discussed. Archive classification: math.PR math.AP math.FA Submitted from: banuelos(a)math.purdue.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.4850 or http://arXiv.org/abs/1012.4850

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Abstract of a paper by D. Azagra, R. Fry, and L. Keener
by alspach＠math.okstate.edu 21 Dec '10

21 Dec '10

This is an announcement for the paper "Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space" by D. Azagra, R. Fry, and L. Keener. Abstract: Let $X$ be a separable real Hilbert space. We show that for every Lipschitz function $f:X\rightarrow\mathbb{R}$, and for every $\varepsilon>0$, there exists a Lipschitz, real analytic function $g:X\rightarrow\mathbb{R}$ such that $|f(x)-g(x)|\leq \varepsilon$ and $\textrm{Lip}(g)\leq \textrm{Lip}(f)+\varepsilon$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 7 pages Submitted from: dazagra(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.4339 or http://arXiv.org/abs/1012.4339

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Abstract of a paper by Spiros A. Argyros and Giorgos Petsoulas
by alspach＠math.okstate.edu 21 Dec '10

21 Dec '10

This is an announcement for the paper "A $c_0$ saturated Banach space with tight structure" by Spiros A. Argyros and Giorgos Petsoulas. Abstract: It is shown that variants of the HI methods could yield objects closely connected to the classical Banach spaces. Thus we present a new $c_0$ saturated space, denoted as $\mathfrak{X}_0$, with rather tight structure. The space $\mathfrak{X}_0$ is not embedded into a space with an unconditional basis and its complemented subspaces have the following structure. Everyone is either of type I, namely, contains an isomorph of $\mathfrak{X}_0$ itself or else is isomorphic to a subspace of $c_0$ (type II). Furthermore for any analytic decomposition of $\mathfrak{X}_0$ into two subspaces one is of type I and the other is of type II. The operators of $\mathfrak{X}_0$ share common features with those of HI spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B26 Remarks: 24 pages 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/1012.2758 or http://arXiv.org/abs/1012.2758

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Abstract of a paper by Rafal Latala
by alspach＠math.okstate.edu 21 Dec '10

21 Dec '10

This is an announcement for the paper "Weak and strong moments of random vectors" by Rafal Latala. Abstract: We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant. Archive classification: math.PR math.FA Mathematics Subject Classification: Primary 60E15, Secondary 52A40, 60B11 Remarks: 8 pages Submitted from: rlatala(a)mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.2703 or http://arXiv.org/abs/1012.2703

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Abstract of a paper by Taras Banakh and Arkady Leiderman
by alspach＠math.okstate.edu 21 Dec '10

21 Dec '10

This is an announcement for the paper "Uniform Eberlein compactifications of metrizable spaces" by Taras Banakh and Arkady Leiderman. Abstract: We prove that each metrizable space (of cardinality less or equal to continuum) has a (first countable) uniform Eberlein compactification and each scattered metrizable space has a scattered hereditarily paracompact compactification. Each compact scattered hereditarily paracompact space is uniform Eberlein and belongs to the smallest class of compact spaces, that contain the empty set, the singleton, and is closed under producing the Aleksandrov compactification of the topological sum of a family of compacta from that class. Archive classification: math.GN math.FA Mathematics Subject Classification: 54D35, 54G12, 54D30, 54D20 Remarks: 6 pages Submitted from: tbanakh(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1012.0920 or http://arXiv.org/abs/1012.0920

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Abstract of a paper by Olivier Guedon and Emanuel Milman
by alspach＠math.okstate.edu 21 Dec '10

21 Dec '10

This is an announcement for the paper "Interpolating thin-shell and sharp large-deviation estimates For isotropic log-concave measures" by Olivier Guedon and Emanuel Milman. Abstract: Given an isotropic random vector $X$ with log-concave density in Euclidean space $\Real^n$, we study the concentration properties of $|X|$ on all scales, both above and below its expectation. We show in particular that: \[ \P(\abs{|X| -\sqrt{n}} \geq t \sqrt{n}) \leq C \exp(-c n^{\frac{1}{2}} \min(t^3,t)) \;\;\; \forall t \geq 0 ~, \] for some universal constants $c,C>0$. This improves the best known deviation results on the thin-shell and mesoscopic scales due to Fleury and Klartag, respectively, and recovers the sharp large-deviation estimate of Paouris. Another new feature of our estimate is that it improves when $X$ is $\psi_\alpha$ ($\alpha \in (1,2]$), in precise agreement with both estimates of Paouris. The upper bound on the thin-shell width $\sqrt{\Var(|X|)}$ we obtain is of the order of $n^{1/3}$, and improves down to $n^{1/4}$ when $X$ is $\psi_2$. Our estimates thus continuously interpolate between a new best known thin-shell estimate and the sharp large-deviation estimate of Paouris. Archive classification: math.FA Remarks: 27 pages - also resolved the negative moment and deviation estimates, interpolating now between the thin-shell and the Paouris small-ball estimate Submitted from: emanuel.milman(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.0943 or http://arXiv.org/abs/1011.0943

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