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.

Excellent introduction to functional analysis, honed by years of teaching this material Provides a graduate student with a serious introduction to many aspects of modern operator algebras and operator theory Covers various topics in operator theory and operator algebras including Hardy spaces, Toeplitz operators, isometries

Contenu

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.