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.
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ISBN-13
978-3-11-164436-3 (9783111644363)
Schweitzer Klassifikation
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.
