Banach March 2016

banach@mathdept.okstate.edu

3 participants
22 discussions

Abstract of a paper by Sergio A. Perez
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Banach spaces of linear operators and homogeneous polynomials without the approximation property” by Sergio A. Perez. Abstract: We present many examples of Banach spaces of linear operators and homogeneous polynomials without the approximation property, thus improving results of Dineen and Mujica [11] and Godefroy and Saphar [13]. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.05489

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Abstract of a paper by Eleftherios Kastis
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “The parabolic algebra on Banach spaces” by Eleftherios Kastis. Abstract: The parabolic algebra was introduced by Katavolos and Power, in 1997, as the operator algebra acting on $L_2(R)$ that is weakly generated by the translation and multiplication semigroups. In particular, they proved that this algebra is reflexive and is equal to the Fourier binest algebra, that is, to the algebra of operators that leave invariant the subspaces of the Volterra nest and its analytic counterpart. We prove that a similar result holds for the corresponding algebras acting on $L_p(R)$, where $1<p<\infty$. It is also shown that the reflexive closures of the Fourier binests on $L_p(R)$, are all order isomorphic for $1<p<\infty$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.03426

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Abstract of a paper Hauke Dirksen
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “The best constant in the Khintchine inequality of the Orlicz space $L_{\Phi_2}$ for equidistributed random variables on spheres” by Hauke Dirksen. Abstract: We compute the best constant in the Khintchine inequality for equidistributed random variables on the $N$-sphere in the Orlicz space $L_{\Phi_2}$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.02471

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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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Banach March 2016