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