# 21 novembre 2017: 2 événements

### Mardi 21 novembre 2017 13:45-15:00 - Safoura Zadeh - IMPAN, Varsovie

Isometric algebra isomorphisms between weighted $L^p$-algebras

Résumé : In Chapter 11 of his renowned book, Th\’eorie des op\’erations lin\’eaires, S. Banach gave a description of linear norm preserving operators on the spaces $L^p$ and $l^p$, $1\leq p<\infty,\ p\neq2$. The proofs are not stated completely and the theorems are not given in their full generality. This was fulfilled by J. Lamperti who provided new proofs for a more general theorem ; besides being set in arbitrary ($\sigma$-finite) measure spaces, Lamperti’s result accepts values $p<1$. Later, Parrot and Strichartz, independently, extended Lamperti’s result to convolution $L^p$-algebras. They showed that if $G$ and $H$ are compact topological groups and if $T:L^p(G)\to L^p(H)$, $1\leq p<\infty,\ p\neq 2$, is an isometric algebra isomorphism then there is an isomorphisms of topological groups $\phi:G\to H$, a continuous character $\gamma:G\to(0,+\infty)$ and a constant $c$ such that
$$Tf(y)=c\gamma\circ\phi^-1(y) f\circ\phi^-1(y), \ \ \ (y\in H).$$
In this talk, we give a description of isometric algebra isomorphisms between weighted $L^p$-algebras on locally compact groups. This is based on a join work with Yulia Kuznetsova.

En savoir plus : Séminaire d’Analyse Fonctionnelle

### Mardi 21 novembre 2017 16:30-18:00 -

Séminaire de Philosophie, sciences cognitives, mathématiques : Guy Wallet

Lieu : Amphi A (UFR ST, Besançon)

En savoir plus : Séminaire de Philosophie, sciences cognitives, mathématiques : Guy Wallet