A Course in Operator Theory
About this Title
John B. Conway, University of Tennessee, Knoxville, TN
Publication: Graduate Studies in Mathematics
Publication Year 2000: Volume 21
ISBNs: 978-0-8218-2065-0 (print); 978-1-4704-2076-5 (online)
MathSciNet review: MR1721402
MSC: Primary 47-01; Secondary 46-01
Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, mathematical physics, and more. This text covers the central themes of operator theory, presented with the excellent clarity and style that readers have come to associate with Conway's writing.
Early chapters introduce and review material on $C^*$-algebras, normal operators, compact operators, and non-normal operators. Some of the major topics covered are the spectral theorem, the functional calculus, and the Fredholm index. In addition, some deep connections between operator theory and analytic functions are presented.
Later chapters cover more advanced topics, such as representations of $C^*$-algebras, compact perturbations, and von Neumann algebras. Major results, such as the Sz.–Nagy Dilation Theorem, the Weyl–von Neumann–Berg Theorem, and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory. The last chapter gives an introduction to reflexive subspaces, which along with hyperreflexive spaces, are one of the more successful episodes in the modern study of asymmetric algebras.
Professor Conway's authoritative treatment makes this a compelling and rigorous course text, suitable for graduate students who have had a standard course in functional analysis.
Graduate students and research mathematicians interested in operator theory.
Table of Contents
- Chapter 1. Introduction to C*-algebras
- Chapter 2. Normal operators
- Chapter 3. Compact operators
- Chapter 4. Some non-normal operators
- Chapter 5. More on C*-algebras
- Chapter 6. Compact perturbations
- Chapter 7. Introduction to von Neumann algebras
- Chapter 8. Reflexivity