Banach Algebras and Harmonic Analysis

Arens Products, Factorizations, and Bounded Operators

Mahmoud Filali

• Publisher: De Gruyter
• Year: 2025
• eBook ISBN: 9783111644363
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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.

Table of contents

• Title Page
• Copyright
• Contents
• Frontmatter
• Contents
• Kernels of bounded operators on the classical transfinite Banach sequence spaces
• Beurling’s theorem on locally compact Abelian groups
• On idempotents and the socle of a Banach algebra
• Fréchet algebras with a dominating Hilbert algebra norm
• Relations between ideals of the Figà-Talamanca Herz algebra Ap(G) of a locally compact group G and ideals of Ap(H) of a closed subgroup
• The composition of conditional expectation and multiplication operators
• On the generation of Arveson weakly continuous semigroups
• The semigroup algebra of a foundation semigroup with locally convex topologies and its Arens regularity
• Bohr compactification and Chu duality of non-Abelian locally compact groups
• ℓ1-bases in Banach algebras and Arens irregularities in harmonic analysis
• Right cancellation, factorization, and right isometries
• On spectral synthesis in convolution Sobolev algebras on the real line
• Projective and free matricially normed spaces
• Banach spaces whose algebras of operators are Dedekind-finite but they do not have stable rank one
• Invariant complementation property and fixed-point sets on power bounded elements in the group von Neumann algebra
• Subspaces that can and cannot be the kernel of a bounded operator on a Banach space
• Towards a sheaf cohomology theory for C∗-algebras
• Tame functionals on Banach algebras
• Left ideals of Banach algebras and dual Banach algebras
• Index