November 2014 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Gideon Schechtman
by alspach＠math.okstate.edu 27 Nov '14

27 Nov '14

This is an announcement for the paper "Three observations regarding Schatten p classes" by Gideon Schechtman. Abstract: The paper contains three results, the common feature of which is that they deal with the Schatten $p$ class. The first is a presentation of a new complemented subspace of $C_p$ in the reflexive range (and $p\not= 2$). This construction answers a question of Arazy and Lindestrauss from 1975. The second result relates to tight embeddings of finite dimensional subspaces of $C_p$ in $C_p^n$ with small $n$ and shows that $\ell_p^k$ nicely embeds into $C_p^n$ only if $n$ is at least proportional to $k$ (and then of course the dimension of $C_p^n$ is at least of order $k^2$). The third result concerns single element of $C_p^n$ and shows that for $p>2$ any $n\times n$ matrix of $C_p$ norm one and zero diagonal admits, for every $\varepsilon>0$, a $k$-paving of $C_p$ norm at most $\varepsilon$ with $k$ depending on $\varepsilon$ and $p$ only. Archive classification: math.FA Mathematics Subject Classification: 47B10, 46B20, 46B28 Submitted from: gideon(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.4427 or http://arXiv.org/abs/1411.4427

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Relations Between Banach Space Theory and Geometric Measure Theory workshop, 08 - 12 June 2015, University of Warwick, UK
by Olga Maleva 27 Nov '14

27 Nov '14

1st ANNOUNCEMENT OF THE WORKSHOP Relations Between Banach Space Theory and Geometric Measure Theory 08 - 12 June 2015 University of Warwick United Kingdom Plenary speakers include: Jesus M F Castillo (Universidad de Extremadura) Gilles Godefroy (Université Paris VI) William B Johnson (Texas A&M University) Assaf Naor* (Princeton University) Mikhail Ostrovskii (St.-John's University) Gideon Schechtman (Weizmann Institute) Thomas Schlumprecht (Texas A&M University) *To be confirmed The homepage of the workshop is: http://tinyurl.com/BanachGMT To register please follow the links on the homepage of the workshop. For further information on the workshop please contact the organisers: * David Preiss <d dot preiss at warwick dot ac dot uk> * Olga Maleva <o dot maleva at bham dot ac dot uk> We expect to be able to cover some expenses for a number of participants. Please read more information on the homepage about the funding. We ask to register your attendance at the workshop by 15 April 2015. The Workshop is supported by a European Research Council grant.

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Abstract of a paper by Tomasz Kobos
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

This is an announcement for the paper "Hyperplanes of finite-dimensional normed spaces with the maximal relative projection constant" by Tomasz Kobos. Abstract: The \emph{relative projection constant} $\lambda(Y, X)$ of normed spaces $Y \subset X$ is defined as $\lambda(Y, X) = \inf \{ ||P|| : P \in \mathcal{P}(X, Y) \}$, where $\mathcal{P}(X, Y)$ denotes the set of all continuous projections from $X$ onto $Y$. By the well-known result of Bohnenblust for every $n$-dimensional normed space $X$ and its subspace $Y$ of codimension $1$ the inequality $\lambda(Y, X) \leq 2 - \frac{2}{n}$ holds. The main goal of the paper is to study the equality case in the theorem of Bohnenblust. We establish an equivalent condition for the equality $\lambda(Y, X) = 2 - \frac{2}{n}$ and present several applications. We prove that every three-dimensional space has a subspace with the projection constant less than $\frac{4}{3} - 0.0007$. This gives a non-trivial upper bound in the problem posed by Bosznay and Garay. In the general case, we give an upper bound for the number of $(n-1)$-dimensional subspaces with the maximal relative projection constant in terms of the facets of the unit ball of $X$. As a consequence, every $n$-dimensional normed space $X$ has an $(n-1)$-dimensional subspace $Y$ with $\lambda(Y, X) < 2-\frac{2}{n}$. This contrasts with the seperable case in which it is possible that every hyperplane has a maximal possible projection constant. Archive classification: math.FA Mathematics Subject Classification: Primary 41A35, 41A65, 47A30, 52A21 Remarks: 15 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/1411.6214 or http://arXiv.org/abs/1411.6214

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Abstract of a paper by Jorge Tomas Rodriguez
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

This is an announcement for the paper "On the norm of products of polynomials on ultraproduct of Banach spaces" by Jorge Tomas Rodriguez. Abstract: The purpose of this article is to study the problem of finding sharp lower bounds for the norm of the product of polynomials in the ultraproducts of Banach spaces $(X_i)_{\mathfrak U}$. We show that, under certain hypotheses, there is a strong relation between this problem and the same problem for the spaces $X_i$. Archive classification: math.FA Submitted from: jtrodrig(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.5894 or http://arXiv.org/abs/1411.5894

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Abstract of a paper by Florent Pierre Baudier
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

This is an announcement for the paper "On the $(\beta)$-distortion of countably branching hyperbolic trees" by Florent Pierre Baudier. Abstract: In this note we show that the distortion incurred by a bi-Lipschitz embedding of the countably branching hyperbolic tree of height $N$ into a Banach space admitting a norm satisfying Rolewicz property $(\beta)$ with power type $p>1$ is at least of the order of $\log(N)^{1/p}$. An application of our result gives a quantitative version of the non-embeddability of countably branching hyperbolic trees into reflexive Banach spaces admitting an equivalent asymptotically uniformly smooth norm and an equivalent asymptotically uniformly convex norm from Baudier, Kalton and Lancien. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20, 46B85 Remarks: 5 pages Submitted from: florent(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.3915 or http://arXiv.org/abs/1411.3915

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Abstract of a paper by Tengiz Kopaliani, Nino Samashvili and Shalva Zviadadze
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

This is an announcement for the paper "On the upper and lower estimates of norms in variable exponent spaces" by Tengiz Kopaliani, Nino Samashvili and Shalva Zviadadze. Abstract: In the present paper we investigate some geometrical properties of the norms in Banach function spaces. Particularly there is shown that if exponent $1/p(\cdot)$ belongs to $BLO^{1/\log}$ then for the norm of corresponding variable exponent Lebesgue space we have the following lower estimate $$\left\|\sum \chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}\leq C\|f\|_{p(\cdot)}$$ where $\{Q\}$ defines disjoint partition of $[0;1]$. Also we have constructed variable exponent Lebesgue space with above property which does not possess following upper estimation $$\|f\|_{p(\cdot)}\leq C\left\|\sum \chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}. $$ Archive classification: math.FA Mathematics Subject Classification: 42B35, 42B20, 46B45, 42B25 Remarks: 13 pages Submitted from: sh.zviadadze(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.3461 or http://arXiv.org/abs/1411.3461

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Abstract of a paper by Mikhail I. Ostrovskii
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

This is an announcement for the paper "Metric characterizations of some classes of Banach spaces" by Mikhail I. Ostrovskii. Abstract: The main purpose of the paper is to present some recent results on metric characterizations of superreflexivity and the Radon-Nikod\'ym property. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary 46B85, Secondary: 05C12, 20F67, 30L05, 46B07, 46B22 Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.3366 or http://arXiv.org/abs/1411.3366

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Abstract of a paper by Marek Cuth and Michal Doucha
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

This is an announcement for the paper "Lipschitz-free spaces over ultrametric spaces" by Marek Cuth and Michal Doucha. Abstract: We prove that the Lipschitz-free space over a separable ultrametric space has a monotone Schauder basis and is isomorphic to $\ell_1$. This extends results of A. Dalet using an alternative approach. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B15, 54E35 Submitted from: marek.cuth(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.2434 or http://arXiv.org/abs/1411.2434

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Abstract of a paper by Kasper Green Larsen and Jelani Nelson
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

This is an announcement for the paper "The Johnson-Lindenstrauss lemma is optimal for linear dimensionality reduction" by Kasper Green Larsen and Jelani Nelson. Abstract: For any $n>1$ and $0<\varepsilon<1/2$, we show the existence of an $n^{O(1)}$-point subset $X$ of $\mathbb{R}^n$ such that any linear map from $(X,\ell_2)$ to $\ell_2^m$ with distortion at most $1+\varepsilon$ must have $m = \Omega(\min\{n, \varepsilon^{-2}\log n\})$. Our lower bound matches the upper bounds provided by the identity matrix and the Johnson-Lindenstrauss lemma, improving the previous lower bound of Alon by a $\log(1/\varepsilon)$ factor. Archive classification: cs.IT cs.CG cs.DS math.FA math.IT Submitted from: minilek(a)seas.harvard.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.2404 or http://arXiv.org/abs/1411.2404

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