C*-algebras

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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.

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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
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

CONTINUOUS FIELDS OF CALGEBRAS
211
EXTENSION TO CALGEBRAS OF THE STONE
250
THE ENVELOPING VON NEUMANN ALGEBRA OF
264
INDEX OF NOTATION
401
SUPPLEMENTARY BIBLIOGRAPHY
485
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