A Course in Operator Theory / Edition 1

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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.

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Editorial Reviews

Covers subjects central to operator theory, with chapters on C*- algebras, normal operators, compact operators, ideals of operators, non-normal operators, compact perturbations, Von Neumann algebras, and reflexivity. Includes examples and applications. Assumes knowledge of fundamental functional analysis. Can be used as a sequel to a basic functional analysis course or as a foundation for the study of operator theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780821820650
  • Publisher: American Mathematical Society
  • Publication date: 11/1/1999
  • Series: Graduate Studies in Mathematics Series , #21
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 372
  • Product dimensions: 70.00 (w) x 10.00 (h) x 1.00 (d)

Table of Contents

Ch. 1 Introduction to C[superscript *]-Algebras 1
Ch. 2 Normal Operators 37
Ch. 3 Compact Operators 71
Ch. 4 Some Non-Normal Operators 105
Ch. 5 More on C[superscript *]-Algebras 181
Ch. 6 Compact Perturbations 207
Ch. 7 Introduction to Von Neumann Algebras 241
Ch. 8 Reflexivity 319
Bibliography 355
Index 367
List of Symbols 371
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