Groups and Operator Algebras Seminar

Speaker: Anders Karlsson (University of Geneva)

Title: An isometry fixed-point theorem and its consequences for operators

Abstract: First I will explain that every isometry of a metric space has a fixed point in a natural compactification. This implies in particular a new mean ergodic theorem, which includes von Neumann's theorem and applies to any Banach space where the usual formulation fails. Second, any invertible element of a C*-algebra acts by isometry on the associated symmetric spaces of positive operators. The fixed point theorem then provides a nontrivial metric eigenfunctional to any invertible element, even when the spectral theorem does not apply.