October 2015 - 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!

1 1

Informal Analysis Seminar at Kent State, November 14-15.
by Artem Zvavitch 14 Mar '16

14 Mar '16

Dear Colleague, The Analysis group at Kent State University is happy to announce a meeting of the Informal Analysis Seminar, which will be held at the Department of Mathematical Sciences at Kent State University, November 14-15, 2015. The plenary lecture series will be given by: Boaz Klartag (Tel Aviv University) and Igor Rivin (University of St. Andrews) Each speaker will deliver a four hour lecture series designed to be accessible for graduate students. Funding is available to cover the local and travel expenses of a limited number of participants. Graduate students, postdoctoral researchers, and members of underrepresented groups are particularly encouraged to apply for support. A poster session will be held for researchers to display their work. Graduate students are particularly encouraged to submit a poster. Posters can be submitted electronically in PDF format before November 6, 2015. Further information, and an online registration form, can be found online http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/Novem… We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please, register before October 1, 2015. Please feel free to contact us at informal(a)math.kent.edu for any further information. Sincerely, Analysis Group at Kent State University

1 1

Abstract of a paper by Sofiya Ostrovska and Mikhail I. Ostrovskii
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Distortion in the finite determination result for embeddings of finite metric spaces into Banach spaces" by Sofiya Ostrovska and Mikhail I. Ostrovskii. Abstract: Given a Banach space $X$ and a locally finite metric space $A$, it is known that if all finite subsets of $A$ admit bilipschitz embeddings into $X$ with distortions $\le C$, then the space $A$ itself admits an embedding into $X$ with distortion $\le D\cdot C$, where $D$ is an absolute constant. The goal of this paper is to show that $D>1$, implying that, in general, there is a ``deterioration of distortion'' in the aforementioned situations. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B85, 46B20 Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.05974 or http://arXiv.org/abs/1510.05974

1 0

Abstract of a paper by Martino Lupini
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Fraisse limits in functional analysis" by Martino Lupini. Abstract: We provide a unified approach to many Fra\"{\i}ss\'{e} limits in functional analysis, including the Gurarij space, the Poulsen simplex, and their noncommutative analogs. We recover in this general framework many classical results about the Gurarij space and the Poulsen simplex, and at the same time obtain their noncommutative generalizations. Particularly, we construct noncommutative analogs of universal operators in the sense of Rota. Archive classification: math.FA math.LO math.OA Mathematics Subject Classification: 46L07, 46A55 (Primary) 46L89, 03C30, 03C98 (Secondary) Remarks: 28 pages Submitted from: lupini(a)caltech.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.05188 or http://arXiv.org/abs/1510.05188

1 0

Abstract of a paper by D.I. Florentin, V. D. Milman, and A. Segal
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Identifying Set Inclusion by Projective Positions and Mixed Volumes" by D.I. Florentin, V. D. Milman, and A. Segal. Abstract: We study a few approaches to identify inclusion (up to a shift) between two convex bodies in ${\mathbb R}^n$. To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or surface area of all projective positions of the sets. We prove similar results for Minkowski sums of the sets. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A05, 52A20, 52A38, 52A39, 51N15, 46B20 Citation: Identifying Set Inclusion by Projective Positions and Mixed The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.03844 or http://arXiv.org/abs/1510.03844

1 0

Abstract of a paper by Martin Dolezal, Martin Rmoutil, Benjamin Vejnar, and Vaclav Vlasak
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Haar meager sets revisited" by Martin Dolezal, Martin Rmoutil, Benjamin Vejnar, and Vaclav Vlasak. Abstract: In the present article we investigate Darji's notion of Haar meager sets from several directions. We consider alternative definitions and show that some of them are equivalent to the original one, while others fail to produce interesting notions. We define Haar meager sets in nonabelian Polish groups and show that many results, including the facts that Haar meager sets are meager and form a $\sigma$-ideal, are valid in the more general setting as well. The article provides various examples distinguishing Haar meager sets from Haar null sets, including decomposition theorems for some subclasses of Polish groups. As a corollary we obtain, for example, that $\mathbb Z^\omega$, $\mathbb R^\omega$ or any Banach space can be decomposed into a Haar meager set and a Haar null set. We also establish the stability of non-Haar meagerness under Cartesian product. Archive classification: math.GN math.FA Remarks: 19 pages Submitted from: dolezal(a)math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.01613 or http://arXiv.org/abs/1510.01613

1 0

Abstract of a paper by Francisco J. Garcia-Pacheco, Alejandro Miralles, and Daniele Puglisi
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Dual maps and the Dunford-Pettis property" by Francisco J. Garcia-Pacheco, Alejandro Miralles, and Daniele Puglisi. Abstract: We characterize the points of $\left\|\cdot\right\|$-$w^*$ continuity of dual maps, turning out to be the smooth points. We prove that a Banach space has the Schur property if and only if it has the Dunford-Pettis property and there exists a dual map that is sequentially $w$-$w$ continuous at $0$. As consequence, we show the existence of smooth Banach spaces on which the dual map is not $w$-$w$ continuous at $0$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B10 Remarks: 6 pages Submitted from: mirallea(a)uji.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.01531 or http://arXiv.org/abs/1510.01531

1 0

Abstract of a paper by Joel Blot and Philippe Cieutat
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Completeness of Sums of Subspace of Bounded Functions and Applications" by Joel Blot and Philippe Cieutat. Abstract: We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness of the sum of two closed subspaces of the Banach space of bounded functions and apply this result on various pseudo almost periodic spaces and pseudo almost automorphic spaces. Archive classification: math.FA Submitted from: blot(a)univ-paris1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.01160 or http://arXiv.org/abs/1510.01160

1 0

Abstract of a paper by Guillaume Aubrun and Stanislaw Szarek
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Dvoretzky's theorem and the complexity of entanglement detection" by Guillaume Aubrun and Stanislaw Szarek. Abstract: The well-known Horodecki criterion asserts that a state $\rho$ on $\mathbb{C}^d \otimes \mathbb{C}^d$ is entangled if and only if there exists a positive map $\Phi : \mathsf{M}_d \to \mathsf{M}_d$ such that the operator $(\Phi \otimes \mathsf{I})(\rho)$ is not positive semi-definite. We show that that the number of such maps needed to detect all the robustly entangled states (i.e., states $\rho$ which remain entangled even in the presence of substantial randomizing noise) exceeds $\exp(c d^3 / \log d)$. The proof is based on a study of the approximability of the set of states (resp. of separable states) by polytopes with few vertices or with few faces, and ultimately relies on the Dvoretzky--Milman theorem about the dimension of almost spherical sections of convex bodies. The result can be interpreted as a geometrical manifestation of the complexity of entanglement detection. Archive classification: quant-ph math.FA Mathematics Subject Classification: 81P40, 46B07 Submitted from: aubrun(a)math.univ-lyon1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.00578 or http://arXiv.org/abs/1510.00578

1 0

Abstract of a paper by Tuomas Hytonen, Sean Li, and Assaf Naor
by alspach＠math.okstate.edu 22 Oct '15

22 Oct '15

This is an announcement for the paper "Quantitative affine approximation for UMD targets" by Tuomas Hytonen, Sean Li, and Assaf Naor. Abstract: It is shown here that if $(Y,\|\cdot\|_Y)$ is a Banach space in which martingale differences are unconditional (a UMD Banach space) then there exists $c=c(Y)\in (0,\infty)$ with the following property. For every $n\in \mathbb{N}$ and $\varepsilon\in (0,1/2]$, if $(X,\|\cdot\|_X)$ is an $n$-dimensional normed space with unit ball $B_X$ and $f:B_X\to Y$ is a $1$-Lipschitz function then there exists an affine mapping $\Lambda:X\to Y$ and a sub-ball $B^*=y+\rho B_X\subseteq B_X$ of radius $\rho\ge \exp(-(1/\varepsilon)^{cn})$ such that $\|f(x)-\Lambda(x)\|_Y\le \varepsilon \rho$ for all $x\in B^*$. This estimate on the macroscopic scale of affine approximability of vector-valued Lipschitz functions is an asymptotic improvement (as $n\to \infty$) over the best previously known bound even when $X$ is $\mathbb{R}^n$ equipped with the Euclidean norm and $Y$ is a Hilbert space. Archive classification: math.FA math.MG Submitted from: naor(a)math.princeton.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1510.00276 or http://arXiv.org/abs/1510.00276

1 0