Banach Algebras and Harmonic Analysis

The book includes recent articles on various topics studied recently in Banach algebras and abstract harmonic analysis. On the Banach algebra side, the reader will find idempotents and socle of a Banach algebra; closed subspaces of a Banach space, including the classical sequence spaces, which are realized as the kernel of a bounded operator; the connection between the stable rank one and Dedekind-finite property of the algebra of operators on a Banach space; spectral synthesis properties in convolution Sobolev algebras on the real line.

The harmonic analysis side includes a generalization of the famous Beurling theorem; groups with few finite-dimensional unitary representations; relations between ideals of the Figa-Talamanca Herz algebra of a locally compact group and ideals of Figa-Talamanca Herz algebra of its closed subgroup; the tame functionals on Banach algebras and in harmonic analysis; and cancellation, factorization, and isometries in algebras on a locally compact group.

The book also includes four surveys written by leaders in the area of full sheaf cohomology theory for noncommutative C - algebras; one-parameter semigroups of bounded operators on a Banach space which are weakly continuous in the sense of Arveson.

• The book offers insights from leading mathematicians on how Banach algebras and abstract harmonic analysis have developed over the last decade.
• The book will be useful to mathematicians and students in many areas of mathematics.

Mahmoud Filali obtained his Phd in 1990 at the university of Sheffield, UK. He has since then been working at the university of Oulu holding different positions; currently he is a lecturer. His research focuses on Banach algebras, semigroup compactifications and harmonic analysis. He has supervised four Phds at his home university and co-supervised one Phd outside his university. He is the editor of a number of journals including his own university journal Acta Universitatis Ouluensis. He has published over sixty articles, co-authored one book and edited two conference proceedings.