Logarithms of Invertible Isometries, Spectral Decompositions and Ergodic Multipliers

Abstract

Firstly, we consider when certain invertible isometries on Banach spaces have (bounded linear) logarithms and when they are trigonometrically well bounded, i.e., have spectral decompositions similar to that of a unitary operator. We then survey aspects of the theory of trigonometrically well-bounded operators, including an outline of some recent results.