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
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
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