### Alberto Salguero Alarcón: Kalton, Peck and Fourier: construction of centralizers over the convolution algebra.

Data: sexta-feira, 5 de novembro de 2021, às 9h30.

Palestrante:
Resumo:  A twisted sum of two Banach spaces $X$ and $Y$ is another space $Z$ containing $Y$ as a closed subspace so that $Z/Y=X$. Perhaps even more interesting is the case in where $X$ and $Y$ are, additionally, Banach modules over a certain Banach algebra $A$. The first question in this direction is whether the twisted sum space $Z$ inherits such $A$-module structure. The case $A=L_\infty$ has been deeply studied and gives rise to the well-known $L_\infty$-centralizers. In this talk, we employ some Fourier analysis techniques, together with properties of $L_\infty$-centralizers, to construct examples of centralizers over the convolution algebra $L_1$. This is part of a joint work with Félix Cabello Sánchez.