Banach

banach@mathdept.okstate.edu

2549 discussions

Banach spaces webinar on Friday 3/5 by Antonio Avilés López (Universidad de Murcia)
by Sari, Bunyamin 04 Mar '21

04 Mar '21

Hello, The next Banach spaces webinar is on Friday March 5 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Antonio Avilés López, Universidad de Murcia Title: Sequential octahedrality and L-orthogonal elements Abstract: Given a Banach space $X$, we consider the following two isometric properties, variations on the notion of octahedrality that can be traced back to the work of B. Maurey: 1. There is an element $e^{**}$ in the sphere of the bidual such that $\|e^{**}+x\| = 1 + \|x\|$ for every $x\in X$. 2. There is a sequence $(e_n)$ in the sphere of $X$ such that $\lim_n \|e_n+x\| = 1 + \|x\|$ Uncountable sums provide examples that 1 does not imply 2. But the converse is unclear. It is natural to conjecture that a weak$^*$-cluster point of the sequence $(e_n)$ would give the desired $e^{**}$. This turns out to be independent of the usual axioms of set theory. The proof involves understanding different kinds of ultrafilters that may or may not exist, as well as a filter version of the Lebesgue dominated convergence theorem, similar to those considered by V. Kadets and A. Leonov. This is a joint work (in progress) with G. Mart\'{\i}nez Cervantes and A. Rueda Zoca. For more information about the past and future 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 on Friday 2/26 by Ben Wallis (Kishwaukee College)
by Sari, Bunyamin 25 Feb '21

25 Feb '21

Hello, The next Banach spaces webinar is on Friday February 26 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Ben Wallis (Kishwaukee College) Title: Garling and Lorentz Sequence Spaces Abstract. We survey some recent results of Garling and Lorentz sequence spaces. Namely, we show that Garling sequence spaces have a unique subsymmetric basis which is not symmetric, are complementably homogeneous, and uniformly complementably lp-saturated. We also exhibit, under certain conditions, a chain of uncountably many closed ideals in its operator algebra, and then do the same for the Lorentz sequence spaces. Finally, we find a nontrivial complemented subspace which is not isomorphic to lp. For more information about the past and future 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 2/19 by Sophie Grivaux (University of Lille)-note the new zoom link
by Sari, Bunyamin 18 Feb '21

18 Feb '21

Hello, The next Banach spaces webinar is on Friday February 19 at 9AM Central time. Please join us at https://yorku.zoom.us/j/92333379646?pwd=MkNyYWpmYTg3VWN3S2dON1kxU0pwdz09<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fyorku.zoo…> Note: Please use the above link not the usual webinar link. Moreover, if you receive an automated reminder email an hour before the talk please ignore it. We are experiencing an unprecedented winter storm in TX and all school systems are down so I cannot access to the webinar account. Thank you to Pavlos Motakis for hosting this week! ********************************** Speaker: Sophie Grivaux (University of Lille) Title: Typical properties of contractions on $\ell_p$-spaces Abstract: Given a separable Banach space $X$ of infinite dimension, one can consider on the space $\mathcal{B}(X)$ of bounded linear operators on $X$ several natural topologies which turn the closed unit ball $B_1(X)=\{T\in\mathcal{B}(X);||T||\le 1\}$ into a Polish space, i.e. a separable and completely metrizable space. In these talk, I will present some results concerning typical properties in the Baire Category sense of operators of $B_1(X)$ for these topologies when $X$ is a $\ell_p$-space, our main interest being to determine whether typical contractions on these spaces have a non-trivial invariant subspace or not. For more information about the past and future 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 on Friday 2/12 by Mikael de la Salle (ENS Lyon)
by Sari, Bunyamin 09 Feb '21

09 Feb '21

Hello, The next Banach spaces webinar is on Friday February 12 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Mikael de la Salle (ENS Lyon) Title: On a duality between Banach spaces and operators Abstract: Most classical local properties of a Banach spaces (for example type or cotype, UMD) are defined in terms of the boundedness of vector-valued operators between Lp spaces or their subspaces. It was in fact proved by Hernandez in the early 1980s that this is the case of any property that is stable by Lp direct sums and finite representability. His result can be seen as one direction of a bipolar theorem for a non-linear duality between Banach spaces and operators. I will present the other direction and describe the bipolar of any class of operators for this duality. The talk will be based on my recent preprint arxiv:2101.07666. For more information about the past and future 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 on Friday 2/5 by Sheng Zhang (Southwest Jiatong University)
by Sari, Bunyamin 04 Feb '21

04 Feb '21

Hello, The next Banach spaces webinar is on Friday February 5 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Sheng Zhang (Southwest Jiaotong University) Title: A metric characterizaion of Rolewicz's property ($\beta$) Abstract: In this talk we will give a new metric characterization of the class of Banach spaces admitting an equivalent norm of Rolewicz's property ($\beta$). Applications regarding the stability of property ($\beta$) under coarse Lipschitz embeddings and nonlinear quotients will be discussed. . For more information about the past and future 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 on Friday 1/22 by Ramón Aliaga (Universitat Politècnica de València)
by Sari, Bunyamin 21 Jan '21

21 Jan '21

Hello, The next Banach spaces webinar is on Friday January 22 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Ramón Aliaga (Universitat Politècnica de València) Title: The Radon-Nikodým and Schur properties in Lipschitz-free spaces Abstract: In this talk I will sketch the proof that, for Lipschitz-free spaces $\mathcal{F}(M)$ over complete metric spaces $M$, several Banach space properties are equivalent including the Radon-Nikodým property, the Schur property, the Krein-Milman property, or not containing copies of $L_1$. These properties hold exactly when $M$ is a purely 1-unrectifiable metric space. For compact $M$, these properties are also equivalent to $\mathcal{F}(M)$ being a dual Banach space. The talk will be based on joint work with C. Gartland, C. Petitjean and A. Procházka. For more information about the past and future 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 on Friday 1/15 by Richard Lechner (JKU Linz)
by Sari, Bunyamin 14 Jan '21

14 Jan '21

Hello, The next Banach spaces webinar is on Friday January 15 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Richard Lechner (Johannes Kepler Universität Linz) Title: Restriced invertibility, subsymmetric bases and factorization Abstract: Given an unconditional normalized basis $(e_j)_{j=1}^n$ of a Banach space $X_n$, we consider conditions under which an operator $T\colon X_n\to X_n$ with ``large diagonal'' can be inverted when restricted to $X_\sigma = [e_j : j\in\sigma]$ for a ``large'' set $\sigma\subset \{1,\ldots,n\}$ (restricted invertibility). We then discuss restricted invertibility and its close connection to finite dimensional quantitative factorization. In the second part of the talk, we show that subsymmetric Schauder bases $(e_j)$ of an infinite dimensional Banach space $X$ have the factorization property, i.e.\@ the identity $I_X$ on $X$ factors through every bounded operator $T\colon X\to X$ with large diagonal. In Banach spaces with a Schauder basis, this type of result can often be proved using gliding-hump techniques, but in non-separable Banach spaces gliding-hump techniques seem unfeasible. However, if $(e_j^*)$ is a non-$\ell^1$-splicing (there is no disjointly supported $\ell^1$-sequence in $X$) subsymmetric weak$^*$ Schauder basis for the dual $X^*$ of $X$, $(e_j^*)$ also has the factorization property. For more information about the past and future 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 on Friday 1/8 by Bill Johnson
by Sari, Bunyamin 06 Jan '21

06 Jan '21

Happy New Year to you all! The first talk of the year is by the one and only Bill Johnson on Friday January 8 at 9AM Central time! Please join us at (note the new zoom ID) https://unt.zoom.us/j/83807914306 Speaker: Bill Johnson, Texas A&M Title: Homomorphisms from L(\ell_p) and L(L_p) (Joint work with N. C. Phillips and G. Schechtman) For more information about the past and future 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 tomorrow 12/15 by Keith Ball-slight time change
by Sari, Bunyamin 14 Dec '20

14 Dec '20

Dear all, This seminar (the original announcement is below) will start 30 minutes later at 10:30AM CDT to avoid time conflict with AGA seminar. 10:30AM CDT 4:30pm London 5:30pm Paris, Berlin, Prague 6:30pm Jerusalem Hope to see you then. Best regards, Bunyamin *************** Dear all, We have a special talk on Tuesday, December 15 at 10AM CDT (please note the unusual day and time). The talk is a tribute to the greatest Jean Bourgain who passed away almost 2 years ago on December 22, 2018. Please join us at https://unt.zoom.us/j/512907580 Speaker: Keith Ball, University of Warwick Title: Restricted Invertibility Abstract: I will briefly discuss the Kadison-Singer problem and then explain a beautiful argument of Bourgain and Tzafriri that I will include in a forthcoming article in a volume dedicated to Jean Bourgain. For more information about the past and future 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 on Tuesday 12/15 (note the unusual time) by Keith Ball (Warwick)
by Sari, Bunyamin 11 Dec '20

11 Dec '20

Dear all, We have a special talk on Tuesday, December 15 at 10AM CDT (please note the unusual day and time). The talk is a tribute to the greatest Jean Bourgain who passed away almost 2 years ago on December 22, 2018. Please join us at https://unt.zoom.us/j/512907580 Speaker: Keith Ball, University of Warwick Title: Restricted Invertibility Abstract: I will briefly discuss the Kadison-Singer problem and then explain a beautiful argument of Bourgain and Tzafriri that I will include in a forthcoming article in a volume dedicated to Jean Bourgain. For more information about the past and future 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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