Banach April 2021

banach@mathdept.okstate.edu

1 participants
3 discussions

Banach spaces webinar on Friday 4/30 by Beata Randrianantoanina (Miami University in Ohio)
by Sari, Bunyamin 29 Apr '21

29 Apr '21

Hello, The next Banach spaces webinar is on Friday April 30 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Beata Randrianantoanina (Miami University in Ohio) Title: On $L_1$-embeddability of unions of $L_1$-embeddable metric spaces and of twisted unions of hypercubes Abstract: Let $\mathcal{E}$ be a class of metric spaces, $(X,d)$ be a metric space, and $A,B$ be metric subspaces of $X$ such that $X=A\cup B$ and $(A,d), (B,d)$ embed bilipschitzly into spaces $E_A,E_B\in \mathcal{E}$ with distortions $D_A, D_B$, respectively. Does this imply that there exists a constant $D$ depending only on $D_A, D_B$, and the class $\mathcal{E}$, so that $(X,d)$ embeds bilipschitzly into some space $E_X\in \mathcal{E}$ with distortion $D$? This question was answered affirmatively for the class $\mathcal{E}$ of all ultrametric spaces by Mendel and Naor in 2013, and for the class $\mathcal{E}$ of all Hilbert spaces by K. Makarychev and Y. Makarychev in 2016. K. Makarychev and Y. Makarychev in 2016 conjectured that the answer is negative when $\mathcal{E}$ is a class of $\ell_p$-spaces for any fixed $p\notin\{2,\infty\},$ in particular for $p=1$. In this connection, Naor in 2015 and Naor and Rabani in 2017 asked whether the metric space known as ``twisted union of hypercubes'', first introduced by Lindenstrauss in 1964, and also considered by Johnson and Lindenstrauss in 1986, embeds into $\ell_1$. In this talk I will show how to embed general classes of twisted unions of $L_1$-embeddable metric spaces into $\ell_1$, including twisted unions of hypercubes whose metrics are determined by concave functions of the $\ell_1$-norm, and discuss some related results (joint work with Mikhail I. Ostrovskii). 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 4/23 by March Boedihardjo (UCLA)
by Sari, Bunyamin 21 Apr '21

21 Apr '21

Hello, The next Banach spaces webinar is on Friday April 23 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: March Boedihardjo (UCLA) Title: Spectral norms of Gaussian matrices with correlated entries Abstract: We give a non-asymptotic bound on the spectral norm of a d×d matrix X with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cases, this estimate is sharp and removes the sqrt(log d) factor in the noncommutative Khintchine inequality. Joint work with Afonso Bandeira. 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 4/9 by Valentin Ferenczi (Universidade de São Paulo)
by Sari, Bunyamin 06 Apr '21

06 Apr '21

Hello, The next Banach spaces webinar is on Friday April 9 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Speaker: Valentin Ferenczi, Universidade de São Paulo Title: There is no largest proper operator ideal Abstract: An operator ideal $U$ (in the sense of Pietsch) is proper if $Space(U)$, the class of spaces $X$ for which $Id_X \in U$, is reduced to the class of finiite-dimensional spaces. Equivalently, $U$ is proper if $U(X)$ is a proper ideal of $L(X)$ whenever $X$ is infinite dimensional (where $U(X)$ denotes the set of operators on $X$ which belong to $U$). We answer a question posed by Pietsch in 1979 by proving that there is no largest proper operator ideal. Our proof is based on an extension of the construction by Aiena-Gonz\'alez (2000), of an improjective but essential operator on Gowers-Maurey's shift space (1997), through a new analysis of the algebra of operators on powers of the shift space. Supported by FAPESP, project 2016/25574-8, and CNPq, grant 303731/2019-2 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 April 2021