Banach

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2549 discussions

Abstract of a paper by Piotr Koszmider, Saharon Shelah and Michal Swietek
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “There is no bound on sizes of indecomposable Banach spaces” by Piotr Koszmider, Saharon Shelah and Michal Swietek. Abstract: Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as$X\oplus Y$, then one of the closed subspaces $X$ or $Y$ must be finite dimensional. It requires alternative techniques compared to those which were initiated by Gowers and Maurey or Argyros with the coauthors. This is because hereditarily indecomposable Banach spaces always embed into $\ell_{\infty}$ and so their density and cardinality is bounded by the continuum and because dual Banach spaces of densities bigger than continuum are decomposable by a result due to Heinrich and Mankiewicz. The obtained Banach spaces are of the form $C(K)$ for some compact connected Hausdorff space and have few operators in the sense that every linear bounded operator $T$ on $C(K)$ for every $f\in C(K)$ satisfies $Tf=gf +S(F)$where $g\in C(K)$ and $S$ is weakly compact or equivalently strictly singular. In particular, the spaces carry the structure of a Banach algebra and in the complex case even the structure of a $C^*$-algebra. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.01753

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Abstract of a paper Colin Petitjean
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Linear structure of Lipschitz-free spaces over countable compact metric spaces” by Colin Petitjean. Abstract: In this paper we show that the Lipschitz-free space over a countable compact metric space linearly embeds into a $\ell_1$-sum of finite dimensional subspaces of itself. Therefore, as a corollary, we will obtain that the Lipschitz-free space over a countable compact metric space has the $1$-Schur property and the $1$-strong Schur property. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.01391

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Abstract of a paper by Kevin Beanland and Ryan Casusey.
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “On a generalization of Bourgain’s tree index” by Kevin Beanland and Ryan Casusey. Abstract: For a Banach space $X$, a sequence of Banach spaces $(Y_n)$, and a Banach space $Z$ with an unconditional basis, D. Alspach and B. Sari introduced a generalization of a Bourgain tree called a $(\oplus_n Y_n)_Z$-tree in $X$. These authors also prove that any separable Banach space admitting a $(\oplus_n Y_n)_Z$-tree with order $\omega_1$ admits a subspace isomorphic to $(\oplus_n Y_n)_Z$. In this paper we give two new proofs of this result. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.01133

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Abstract of a paper by Antonin Prochazka
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Linear properties of Banach spaces and low distortion embeddings of metric graphs” by Antonin Prochazka. Abstract: We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $1+\epsilon$-isomorphic to a subspace of a Banach space $X$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.00741

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Abstract of a paper by Daniel Azagra and Carlos Mudarra
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “An Extension Theorem for convex functions of class $C^{1,1}$ on Hilbert spaces” by Daniel Azagra and Carlos Mudarra. Abstract: Let $H$ be a Hilbert space, $E\subset H$ be an arbitrary subset and $f : E\rightarrow R, G: E\rightarrow H$ be two functions. We give a necessary and sufficient condition on the pair $(f, G)$ for the existence of a convex function $F\in C^{1,1}(H)$ such that $F=f$ and $\nabla F= G$ on $E$. We also show that, if this condition is met, $F$ can be taken so that Lip$(\nabla F)=$Lip$(G)$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.00241

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Transfinite methods in Banach spaces and algebras of operators
by Bentuo Zheng (bzheng) 16 Mar '16

16 Mar '16

Dear colleague, We are pleased to announce that registration has now opened for the conference "Transfinite methods in Banach spaces and algebras of operators", to be held in Bedlewo, Poland, 18-22 July 2016. To register, please go to the conference webpage and follow the links: https://www.impan.pl/~set_theory/Banach2016/ There is a registration fee of 900PLN (approx. €210), which includes room and full board for the duration of the conference.Important dates: 15 April: deadline for graduate students to apply for financial support to cover their local expenses (see the webpage for full details); 31 May: registration to the conference closes (may happen earlier, if all rooms at the conference centre fill up); 24 June : deadline for submission of abstracts of contributed talks. Main speakers are: Tristan Bice (Salvador), Christina Brech (São Paulo), Yemon Choi (tbc)(Lancaster), Marek Cuth (Prague), Garth Dales (Lancaster), Alan Dow (North Carolina), Valentin Ferenczi (São Paulo), Joanna Garbulińska (Kielce), Gilles Godefroy (CNRS), Bill Johnson (tbc) (Texas A&M), Tomasz Kochanek (IM PAN, Warsaw), Jordi Lopez-Abad (ICMAT Madrid), Pavlos Motakis (Texas A&M), Grzegorz Plebanek (Wrocław), Thomas Schlumprecht (Texas A&M), David Sherman (tbc)(Virginia), Jesus Suarez (Caceres), Stevo Todorcevic (CNRS, Toronto). If you have any questions, please look at the webpage, or write to this address (possibly NOT replying to this e-mail). Best regards, the organizers (Antonio Aviles, Piotr Koszmider, Niels Laustsen)

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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

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VI Int. Conference in Optimization Theory and its Applications (ALEL) + IV Workshop on Functional Analysis
by Luis Carlos García Lirola 12 Mar '16

12 Mar '16

1st ANNOUNCEMENT OF THE COMMON EVENTS: VI INT. CONFERENCE IN OPTIMIZATION THEORY AND ITS APPLICATIONS (ALEL) + IV WORKSHOP ON FUNCTIONAL ANALYSIS June 6th – June 10th, Cartagena (Spain) The ALEL will take place from the June 6 to 8. In its sixth edition, it is co-organized by the universities of Alicante, Cartagena, Limoges, Miguel Hernández (Elche) and Murcia. The aim of the meeting is to promote the connection and exchange of knowledge among researchers from different countries on topics like convex and non-smooth analysis, numerical methods or semi-infinite optimization. There will be a number of (non-parallel) invited talks given by the following speakers: Paul Armand, Loïc Bourdin, Jean-Baptiste Caillau, Thai Doan Chuong, Robert Deville, Asen Dontchev, Jesús García Falset, Sorin-Mihai Grad, Abderrahim Hantoute, Jean-Baptiste Hiriart-Urruty, Nouredine Igbida, Abderrahim Jourani, Yalcin Kaya, Mathieu Kessler, Diethard Klatte, Guoyin Li, Boris Mordukhovic, Mikhail Ostrovskii, Daniele Puglisi, David Salas Videla, Francisco Silva, Mikhail Solodov, Jarno Talponen, Shawn Wang, Darius Zagrodny. A poster session will be held for (especially young) researchers to display their work. The ALEL will be followed from June 9 to 10 by the fourth edition of the Workshop on Functional Analysis organized by the research group of Functional Analysis of the UM. Gathering of experienced and novice researchers with interest in Banach space theory, the meeting will consist of a series of short talks as well as plenary talks given by the following speakers: Daniel Azagra, Jonathan Borwein, Gilles Godefroy, Petr Hajek, Natalia Jonard, Vladimir Kadets, Denka Kutzarova (to be confirmed), Tony Prochazka, Daniele Puglisi, Clemente Zanco. Both meetings will be held in the millenarian seaside city of Cartagena, more specifically, in the historic building of the Polytechnic University of Cartagena, former Instruction Center of Army, and currently occupied by the Naval Museum and the Faculty of Business. It is located opposite the port, closed to hotels and the pedestrian area of the city. For registration and details about travel and accommodation, we refer to the respective homepages of the meetings: http://www.um.es/beca/alel2016/ http://www.um.es/beca/workshop2016/ For more information, please contact Matías Raja <matias(at)um.es>. On behalf of the organizing committee: Carlos Angosto, Luis Oncina, Antonio Pallarés and Matías Raja.

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Conference on Functional Analysis in Honour of Nicole Tomczak-Jaegermann
by Bentuo Zheng (bzheng) 08 Mar '16

08 Mar '16

It is our pleasure to announce the Conference on Functional Analysis in Honour of Nicole Tomczak-Jaegermann to be held at the University of Alberta, Edmonton, AB, Canada, May 16 - 20, 2016. http://www.math.ualberta.ca/~vtroitsky/nicolefest/ You are cordially invited to participate in the meeting. Please let us know at your earliest convenience whether you are planning to attend the conference. Please feel free to pass the information about the conference to anyone else. Best wishes, Local organizers (Alexander Litvak, Vladimir Troitsky, Vlad Yaskin)

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[Banach Space Bulletin Board] Abstract of a paper by Christian Bargetz, Michael Dymond and Simeon Reich
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Porosity Results for Sets of Strict Contractions on Geodesic Metric Spaces” by Christian Bargetz, Michael Dymond and Simeon Reich. Abstract: We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $CAT(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in these settings. We prove that the strict contractions form a negligible subset of this space in the sense that they form a $\sigma$-porous subset. For separable metric spaces we show that a generic nonexpansive mapping has Lipschitz constant one at typical points of its domain. These results contain the case of nonexpansive self-mappings and the case of nonexpansive set-valued mappings as particular cases. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.05230

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