Functional Analysis and Operator Algebras

By: Kenneth R. Davidson

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eText | 9 April 2025

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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.