Functional Analysis and Operator Algebras

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.

List of 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.

Product details

• Authors: Kenneth Davidson, Kenneth R Davidson, Kenneth R. Davidson
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 19.10.2024
• EAN: 9783031636646
• ISBN: 978-3-0-3163664-6
• No. of pages: 797
• Dimensions: 155 mm x 47 mm x 235 mm
• Weight: 1310 g
• Illustrations: XIV, 797 p. 3 illus., 2 illus. in color.
• Series: CMS/CAIMS Books in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Functional Analysis, Operator Theory, Banach algebras, Toeplitz operators, Choquet theory