January 2021 - Banach - mathdept.okstate.edu

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

1 0

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

1 0

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

1 0