February 2021 - Banach - mathdept.okstate.edu

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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