April 2020 - Banach - mathdept.okstate.edu

Banach spaces webinar reminder tomorrow, software update, and a correction
by Sari, Bunyamin 30 Apr '20

30 Apr '20

Dear all, 1. A quick reminder for tomorrow’s talk. Dan Freeman is speaking. 2. Please update your zoom (Go to menu on top and click Check for updates, the new version should be 5.0.1). 3. A correction: In the last sentence of the Dan’s abstract, his collaborator Mitchell Taylor’s last name was cut off. Mitchell is a grad student at Berkeley. Apologies to Mitchell! See the abstract below. See you tomorrow! Bunyamin Friday May 1st 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Dan Freeman, St Louis University Title: A Schauder basis for $L_2$ consisting of non-negative functions Abstract. We will discuss what coordinate systems can be created for $L_p(\mathbb R)$ using only non-negative functions with $1\leq p<\infty$. In particular, we will describe the construction of a Schauder basis for $L_2(\mathbb R)$ consisting of only non-negative functions. We will conclude with a discussion of some related open problems. This is joint work with Alex Powell and Mitchell Taylor.

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Post-doc position at the University of São Paulo
by valentin ferenczi 30 Apr '20

30 Apr '20

Dear colleague, We would like to announce a post-doctoral position in the Department of Mathematics of the University of São Paulo (Brazil) within the scope of Geometry of Banach spaces. This position is for a period of 12 to 24 months and as of today must end on July 31th 2022 (we expect to extend this deadline to January 31th 2023). The initial date of the activities is negotiable, but preferably between August and December 2020, and the deadline to apply is May 31th, 2020. The position is available as part of the FAPESP Thematic Project "Geometry of Banach spaces": https://geometryofbanachspaces.wordpress.com/ The position has no teaching duties and includes a monthly stipend which is, as of September 1, 2018 of BRL 7373,10 (tax free). It also includes partial support for travel and the first expenses upon arrival, as well as Research Contigency Funds equivalent to 15% of the fellowship. All relevant information may be found at https://geometryofbanachspaces.wordpress.com/postdoc-position-open/ Don't hesitate to contact me for additional information. All the best, Valentin.

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Banach spaces webinar on Friday 5/1 by Dan Freeman
by Sari, Bunyamin 27 Apr '20

27 Apr '20

Dear all, The next Banach spaces webinar is on Friday May 1st 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Dan Freeman, St Louis University Title: A Schauder basis for $L_2$ consisting of non-negative functions Abstract. We will discuss what coordinate systems can be created for $L_p(\mathbb R)$ using only non-negative functions with $1\leq p<\infty$. In particular, we will describe the construction of a Schauder basis for $L_2(\mathbb R)$ consisting of only non-negative functions. We will conclude with a discussion of some related open problems. This is joint work with Alex Powell and Mitchell. Upcoming schedule May 8: Chris Gartland, UIUC May 15 Gideon Schechtman Weizmann Institute of Science May 22 Pedro Tradacete Instituto de Ciencias Matemáticas May 29 Miguel Martin University of Granada June 5 Denny Leung National University of Singapore June 12 Noé de Rancourt Kurt Gödel Research Center June 19 Christian Rosendal UIC and NSF June 26 Pete Casazza University of Missouri For more information past talks and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar Friday 4/24 by Tomasz Kania
by Sari, Bunyamin 20 Apr '20

20 Apr '20

Dear all, The next Banach spaces webinar is on Friday April 24 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Tomasz Kania, Czech Academy Title: Quantifying Kottman's constant<http://www.math.unt.edu/~bunyamin/banach#Tomasz%20Kania> Abstract. Kottman's constant, K(X), of a Banach space X is the supremum over those d>0 for which the unit sphere of X contains a d-separated sequence. It is known that K(X)>1 for every infinite-dimensional space X (the Elton–Odell theorem). I will present certain estimates related to interpolation spaces, twisted sums, and other classes of Banach spaces X concerning the isomorphic Kottman constant, defined as the infimum of K(Y), where Y ranges over all renormings of X. I will also comment on other related constants (such as the disjoint one defined for Banach lattices) and their symmetric analogs. This talk is based on papers with J. M. F. Castillo, M, González, P. L. Papini (PAMS 2020+)<https://arxiv.org/abs/1910.01626> and P. Hájek, T. Russo (JFA 2018)<https://arxiv.org/abs/1803.11501>. Upcoming schedule<http://www.math.unt.edu/~bunyamin/banach> May 1 Daniel Freeman<http://www.math.unt.edu/~bunyamin/banach#Daniel%20Freeman> St Louis University May 8 Chris Gartland<http://www.math.unt.edu/~bunyamin/banach#Chris%20Gartland> UIUC May 15 Gideon Schechtman<http://www.math.unt.edu/~bunyamin/banach#Gideon%20Schechtman> Weizmann Institute of Science May 22 Pedro Tradacete<http://www.math.unt.edu/~bunyamin/banach#Pedro%20Tradacete> Instituto de Ciencias Matemáticas May 29 Miguel Martin<http://www.math.unt.edu/~bunyamin/banach#Miguel%20Martin> University of Granada June 5 Denny Leung<http://www.math.unt.edu/~bunyamin/banach#Denny%20Leung> National University of Singapore June 12 Noé de Rancourt<http://www.math.unt.edu/~bunyamin/banach#No%C3%A9%20de%20Rancourt> Kurt Gödel Research Center June 19 Christian Rosendal<http://www.math.unt.edu/~bunyamin/banach#Christian%20Rosendal> UIC and NSF June 26 Pete Casazza<http://www.math.unt.edu/~bunyamin/banach#Pete%20Casazza> University of Missouri The video of last week’s talk is available here <https://youtu.be/ynSsWJwCeQA> * For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach * For a comprehensive list of talks in all areas of maths see the website Math Seminars<https://mathseminars.org/>. Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar Friday 4/17 by Mikhail Ostrovskii
by Sari, Bunyamin 13 Apr '20

13 Apr '20

Dear all, The next Banach spaces webinar is on Friday April 17th 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Mikhail Ostrovskii, St John’s University Title: Transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces, Wasserstein 1 spaces, etc. Abstract. After a brief introduction I shall talk about ℓ1-subspaces in transportation cost spaces. Results presented in this talk, mentioned in it, or related to it, can be found in joint papers with Stephen Dilworth, Seychelle Khan, Denka Kutzarova, Mutasim Mim, and Sofiya Ostrovska, see * Lipschitz free spaces on finite metric spaces<https://arxiv.org/abs/1807.03814> * Generalized transportation cost spaces<https://arxiv.org/abs/1902.10334> * Isometric copies of $\ell^n_{\infty}$ and $\ell_1^n$ in transportation cost spaces on finite metric spaces<https://arxiv.org/abs/1907.01155> * On relations between transportation cost spaces and L_1<https://arxiv.org/abs/1910.03625> Upcoming schedule April 24: Tomasz Kania, Czech Academy May 1: Dan Freeman, St Louis May 8: Chris Gartland, UIUC May 15: Gideon Schechtman, Weizmann Institute of Science The video of last week’s talk is available here https://www.youtube.com/watch?v=oRij6EWzlF4&feature=youtu.be&t=32 * For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach * For a comprehensive list of talks in all areas of maths see the website Math Seminars<https://mathseminars.org/>. Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar Friday 4/10 by Pavlos Motakis
by Sari, Bunyamin 07 Apr '20

07 Apr '20

Dear all, The next Banach spaces webinar is on Friday April 10th 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Pavlos Motakis, The University of Illinois at Urbana–Champaign Title: Coarse Universality Abstract. The Bourgain index is a tool that can be used to show that if a separable Banach space contains isomorphic copies of all members of a class C then it must contain isomorphic copies of all separable Banach spaces. This can be applied, e.g., to the class C of separable reflexive spaces. Notably, the embedding of each member of C does not witness the universality of X. We investigate a natural coarse analogue of this index which can be used, e.g., to show that a separable metric space that contains coarse copies of all members in certain “small" classes of metric spaces C then X contains a coarse copy of $c_0$ and thus of all separable metric spaces. This is joint work with F. Baudier, G. Lancien, and Th. Schlumprecht. Upcoming schedule April 17: Mikhail Ostrovskii, St. John’s April 24: Tomasz Kania, Czech Academy May 1: Dan Freeman, St Louis May 8: Chris Gartland, UIUC The video of last week’s talk is available here https://youtu.be/3U_e0Mc25cs For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Abstract of a paper by Geraldo Botelho, José Lucas P. Luiz
by Bentuo Zheng (bzheng) 01 Apr '20

01 Apr '20

This is an announcement for the paper “The positive polynomial Schur property in Banach lattices” by Geraldo Botelho<https://arxiv.org/search/math?searchtype=author&query=Botelho%2C+G>, José Lucas P. Luiz<https://arxiv.org/search/math?searchtype=author&query=Luiz%2C+J+L+P>. Abstract: We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$-spaces are shown to be positively polynomially Schur, lattice analogues of results on Banach spaces are obtained and relationships with the positive Schur and the weak Dunford-Pettis properties are established. https://arxiv.org/abs/2003.11626

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Abstract of a paper by William B. Johnson, Gideon Schechtman
by Bentuo Zheng (bzheng) 01 Apr '20

01 Apr '20

This is an announcement for the paper ``The number of closed ideals in $L(L_p)$” by William B. Johnson<https://arxiv.org/search/math?searchtype=author&query=Johnson%2C+W+B>, Gideon Schechtman<https://arxiv.org/search/math?searchtype=author&query=Schechtman%2C+G>. Abstract: We show that there are $2^{2^{\aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\not= 2<\infty$. This solves a problem in A. Pietsch's 1978 book "Operator Ideals". The proof is quite different from other methods of producing closed ideals in the space of bounded operators on a Banach space; in particular, the ideals are not contained in the strictly singular operators and yet do not contain projections onto subspaces that are non Hilbertian. We give a criterion for a space with an unconditional basis to have $2^{2^{\aleph_0}}$ closed ideals in term of the existence of a single operator on the space with some special asymptotic properties. We then show that for $1<q<2$ the space ${\frak X}_q$ of Rosenthal, which is isomorphic to a complemented subspace of $L_q(0,1)$, admits such an operator. https://arxiv.org/abs/2003.11414

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Abstract of a paper by R.M. Causey, E. Galego, C. Samuel
by Bentuo Zheng (bzheng) 01 Apr '20

01 Apr '20

This is an announcement for the paper “$c_{0} \widehat{\otimes}_πc_{0}\widehat{\otimes}_πc_{0}$ is not isomorphic to a subspace of $c_{0} \widehat{\otimes}_πc_{0}$ ” by R.M. Causey<https://arxiv.org/search/math?searchtype=author&query=Causey%2C+R+M>, E. Galego<https://arxiv.org/search/math?searchtype=author&query=Galego%2C+E>, C. Samuel<https://arxiv.org/search/math?searchtype=author&query=Samuel%2C+C>. Abstract: In the present paper we prove that the $3$-fold projective tensor product of $c_0$, $c_{0} \widehat{\otimes}_\pi c_{0}\widehat{\otimes}_\pi c_{0}$, is not isomorphic to a subspace of $c_{0} \widehat{\otimes}_\pi c_{0}$. In particular, this settles the long-standing open problem of whether $c_{0} \widehat{\otimes}_\pi c_{0}$ is isomorphic to $c_{0} \widehat{\otimes}_\pi c_{0}\widehat{\otimes}_\pi c_{0}$. The origin of this problem goes back to Joe Diestel who mentioned it in a private communication to the authors of paper "Unexpected subspaces of tensor products" published in 2006. https://arxiv.org/abs/2003.09878

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Abstract of a paper by Jesús M.F. Castillo, Valentin Ferenczi
by Bentuo Zheng (bzheng) 01 Apr '20

01 Apr '20

This is an announcement for the paper “Group actions on twisted sums of Banach spaces” by Jesús M.F. Castillo<https://arxiv.org/search/math?searchtype=author&query=Castillo%2C+J+M+F>, Valentin Ferenczi<https://arxiv.org/search/math?searchtype=author&query=Ferenczi%2C+V>. Abstract: We study bounded actions of groups and semigroups on exact sequences of Banach spaces, characterizing different type of actions in terms of commutator estimates satisfied by the quasi-linear map associated to the exact sequence. As a special and important case, actions on interpolation scales are related to actions on the exact sequence induced by the scale through the Rochberg-Weiss theory. Consequences are presented in the cases of certain non-unitarizable triangular representations of the free group on the Hilbert space, of the compatibility of complex structures on twisted sums, as well as of bounded actions on the interpolation scale of Lp-spaces. As a new fundamental example, the isometry group of Lp(0,1), p different from 2, is shown to extend as an isometry group acting on the associated Kalton-Peck space Zp. Finally we define the concept of G-splitting for exact sequences admitting the action of a semigroup G, and give criteria and examples to relate G-splitting and usual splitting of exact sequences: while both are equivalent for amenable groups and, for example, reflexive spaces, counterexamples are provided where one of these hypotheses is not satisfied. https://arxiv.org/abs/2003.09767

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