Functional Analysis and Operator Algebras / by Kenneth R. Davidson.

Format:

Book

Author/Creator:

Davidson, Kenneth R., Author.

Series:

CMS/CAIMS Books in Mathematics, 2730-6518 ; 13

Language:

English

Subjects (All):

Functional analysis.

Functional Analysis.

Local Subjects:

Functional Analysis.

Physical Description:

1 online resource (XIV, 797 p. 3 illus., 2 illus. in color.)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This book offers a comprehensive introduction to various aspects of functional analysis and operator algebras. In Part I, readers will find the foundational material suitable for a one-semester course on functional analysis and linear operators. Additionally, Part I includes enrichment topics that provide flexibility for instructors. Part II covers the fundamentals of Banach algebras and C*-algebras, followed by more advanced material on C* and von Neumann algebras. This section is suitable for use in graduate courses, with instructors having the option to select specific topics. Part III explores a range of important topics in operator theory and operator algebras. These include $H^p$ spaces, isometries and Toeplitz operators, nest algebras, dilation theory, applications to various classes of nonself-adjoint operator algebras, and noncommutative convexity and Choquet theory. This material is suitable for graduate courses and learning seminars, offering instructors flexibility in selecting topics.

Contents:

Part I Functional Analysis

1 Set Theory and Topology

2 Banach Spaces

3 LCTVSs and Weak Topologies

4 Linear Operators

5 Compact Operators

Part II Banach and C*-algebras

6 Banach Algebras

7 Commutative Banach Algebras

8 Noncommutative Banach Algebras

9 C*-Algebras

10 Von Neumann Algebras

Part III Operator Theory

11 Hardy Spaces

12 Isometries and Toeplitz Operators

13 Nest Algebras

14 Dilation Theory

15 Nonselfadjoint Operator Algebras

16 Noncommutative Convexity.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783031636653

3031636651

OCLC:

1524422190