On a class of Banach algebras associated to harmonic analysis on locally compact groups and semigroups

Document Type: Article dedicated to Uffe Haagerup


University of Alberta


The purpose of this paper is to present some old and recent results for the class of $F$-algebras which include most classes of Banach algebras that are important in abstract harmonic analysis. We also introduce a subclass of the class of $F$-algebras, called normal $F$-algebras, that captures better the measure algebras and the (reduced) Fourier--Stieltjes algebras, and use this to give new characterisations the reduced Fourier--Stieltjes algebras of discrete groups.