Michael Hartz (Saarland University) : Finite dimensional representations of operator algebrasSéminaire « Analyse fonctionnelle »
Orateur: Michael Hartz
Affiliation : Saarland University
Date : 3 Février 2023
Heure : 14h
Lieu : Salle Kampé de Fériet, Bâtiment M2
Titre : Finite dimensional representations of operator algebras
A (non-selfadjoint) operator algebra is said to be residually finite dimensional (RFD) if it can be recovered from its finite dimensional representations. In addition to its abstract relevance, this property plays a role in the study of certain algebras of holomorphic functions. Residual finite dimensionality is well studied in the context of C*-algebras. In particular, a theorem of Exel and Loring characterizes RFD C*-algebras in terms of the state space and in terms of a finite-dimensional approximation property for representations.
I will talk about a non-selfadjoint version of the Exel-Loring theorem. Moreover, I will explain how this is related to a question of Clouatre, Dor-On and Ramsay about the RFD property of the maximal C*-algebra of a non-selfadjoint operator algebra.