C*-algebras

Jacques Dixmier

North-Holland, 1982 - C*-algebras - 513 pages

Almost four-fifths of this book deals with the study of C*-algebras, and the main results due, among others, to Fell, Glimm, Kadison, Kaplansky, Mackey and Segal are expounded. Because of the amount of material accumulated on unitary representations of groups, the latter pages of the book are devoted to a brief account of some aspects of this subject, particularly since the theory of groups provides some of the most interesting examples of C*-algebras. The theory of C*-algebras is still expanding rapidly, but this work remains a clear and accessible introduction to the fundamentals of the subject.

Contents

• NORMED INVOLUTIVE ALGEBRAS: 3
• HAPTE: 26
• LIMINAL CALGEBRAS: 94
• THE TYPE OF A REPRESENTATION: 114
• TRACES AND REPRESENTATIONS: 131
• THE QUASISPECTRUM: 151
• INTEGRATION AND DISINTEGRATION: 162
• CALGEBRAS OF TYPE I: 190
• CONTINUOUS FIELDS OF CALGEBRAS: 211
• EXTENSION TO CALGEBRAS OF THE STONE: 250
• THE ENVELOPING VON NEUMANN ALGEBRA OF: 264
• UNITARY REPRESENTATIONS OF LOCALLY: 279
• SQUAREINTEGRABLE IRREDUCIBLE: 309
• REPRESENTATIONS OF COMPACT GROUPS: 319
• ALMOSTPERIODIC FUNCTIONS: 333
• CHARACTERS OF A LOCALLY COMPACT GROUP: 343
• THE DUAL OF A LOCALLY COMPACT GROUP: 353
• APPENDIX A von Neumann algebras: 374
• APPENDIX B Miscellaneous results: 393
• INDEX OF NOTATION: 401
• SUPPLEMENTARY BIBLIOGRAPHY: 485

Bibliographic information

• Title: C*-algebras; Volume 15 of North-Holland mathematical library, ISSN 0924-6509
• Author: Jacques Dixmier
• Editor: Jacques Dixmier
• Edition: revised
• Publisher: North-Holland, 1982
• Original from: Pennsylvania State University
• Digitized: Aug 25, 2009
• ISBN: 0444863915, 9780444863911
• Length: 513 pages