The Banach algebra M(T)

Abstract

This first chapter is devoted to the study of the Banach algebra M(T). This study will be brief because we need only little about M(T), and there exist excellent books on the subject, in which all the proofs will be found [123, 141, 218, 232]. We introduce the technics of generalized characters to precise the spectral properties of measures such as generalized Riesz products, which will nicely appear later as maximal spectral type of certain dynamical systems. © 2010 Springer-Verlag Berlin Heidelberg.