Banach Algebras and Harmonic Analysis : Arens Products, Factorizations, and Bounded Operators.

Format:

Book

Author/Creator:

Filali, Mahmoud.

Language:

English

Subjects (All):

Banach algebras.

Harmonic analysis.

Physical Description:

1 online resource (314 pages)

Edition:

1st ed.

Place of Publication:

Berlin/Boston : Walter de Gruyter GmbH, 2025.

Summary:

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;.

Contents:

Intro

Preface

Contents

Kernels of bounded operators on the classical transfinite Banach sequence spaces

1 Introduction and main results

2 Preliminaries and the proof of Theorem 1.2

3 Proof of Theorem 1.3

4 Wark's Banach space admits a closed subspace that is not the kernel of any bounded operator on it

Bibliography

Beurling's theorem on locally compact Abelian groups

1 Introduction

2 The theorem

On idempotents and the socle of a Banach algebra

2 Idempotents and the socle

Fréchet algebras with a dominating Hilbert algebra norm

2 Preliminaries

3 Fréchet subalgebras of L*(s)

4 Examples

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

2 On the multipliers of Ap(G)

3 Ideals with bounded approximate unit

4 The image of a closed ideal under the restriction map

The composition of conditional expectation and multiplication operators

1 Introduction and preliminaries

2 Centered and normal weighted conditional type operators

3 Applications

On the generation of Arveson weakly continuous semigroups

2 Arveson weakly continuous one-parameter semigroups

3 The Arveson ideal

4 The generator as a weakly densely defined operator

5 Quasimultipliers on the Arveson ideal and Arveson spectrum

6 Quasimultipliers on the Arveson ideal as weakly densely defined operators

7 The normalized Arveson ideal

8 The generator as a quasimultiplier on the Arveson ideal

9 The Arveson spectrum

10 The resolvent

11 Holomorphic functional calculus

Bibliography.

The semigroup algebra of a foundation semigroup with locally convex topologies and its Arens regularity

3 Dual of Ma(S) with a locally convex topology

4 The second dual of Ma(S) with a locally convex and the topological center of (Ma(S),tLUC)**

Bohr compactification and Chu duality of non-Abelian locally compact groups

3 Self-Bohrifying groups

4 Bohr compactification versus Chu duality

l1-bases in Banach algebras and Arens irregularities in harmonic analysis

2 Some basic definitions and notation

2.1 The space LUC(A)

3 Non-Arens regularity

3.1 What is known on non-Arens regularity in harmonic analysis

3.2 The definitions

4 Extreme non-Arens regularity

4.1 What is known on extreme non-Arens regularity

4.2 The new approach: triangles and l1-bases

4.3 l1(η)-bases in A

4.4 EnArity of general Banach algebras

4.5 Applications: algebras with bai's

4.6 Algebras with weak TI's

4.7 Algebras in harmonic analysis I

4.8 EnArity of preduals of a von Neuman algebras

4.9 Algebras in harmonic analysis II

5 On the strong Arens irregularity of Banach algebras

5.1 What is known on strong Arens irregularity and topological centers

5.2 The new approach: Fl1(η)-bases and factorizations

5.3 Fl1(η)-bases

6 Examples

6.1 Group algebra and measure algebra

6.2 Fourier algebra and Fourier-Stieltjes algebra

7 The algebraic structure of A**, LUC(A)*, and M(A)**

Right cancellation, factorization, and right isometries

2 Results

On spectral synthesis in convolution Sobolev algebras on the real line

2 Derivatives, convolution, and Fourier transform

3 Weak spectral synthesis in Sobolev algebras.

4 Approximation by ideals of spectral synthesis

Projective and free matricially normed spaces

2 Initial definitions

3 Construction of the matricially normed spaces M"310Mn

4 Projectivity and freeness in rigged categories

5 The rig n and its free objects with the one-point base

6 Characterization of free and projective spaces

7 Some properties of the matricially normed space M"310Mn

Banach spaces whose algebras of operators are Dedekind-finite but they do not have stable rank one

1 Introduction and basic terminology

2 Algebras of operators with stable rank one and their connection to Dedekind-finiteness

Invariant complementation property and fixed-point sets on power bounded elements in the group von Neumann algebra

2 Some preliminaries

3 Invariant complementation property of the group von Neumann algebra

4 Fixed-point sets of power bounded elements in VN(G)

5 Some remarks and open problems

5.1 Invariant complementation property

5.2 Natural projections

5.3 Geometric form of the Hahn-Banach separation theorem

5.4 Sets of spectral synthesis

Subspaces that can and cannot be the kernel of a bounded operator on a Banach space

Towards a sheaf cohomology theory for C*-algebras

2 Topology

3 Exact categories

4 Sheaves

5 Our kind of categories

6 OMod8A(X) is exact

7 Homological algebra in OMod8A(X)

Tame functionals on Banach algebras

2 Some definitions: independence and tameness

2.1 Independence and tame systems

2.2 Tame functionals

3 Tame functionals on the group algebra l1(G)

3.1 Tame functions on groups

4 Appendix.

4.1 Background on fragmentability and tame families

4.2 Independent sequences of functions

Left ideals of Banach algebras and dual Banach algebras

3 Examples from abstract harmonic analysis

4 Left and right ideals of approximable operators on a Banach space

5 Multiplier algebras and dual Banach algebras

6 Some classification results

Index.

Notes:

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ISBN:

3-11-164358-1

OCLC:

1531974048