- J. Dixmier
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.
North-Holland Mathematical Library
Published: January 1977
The translation is excellent, and does justice to the original...
As far as readability and thoroughness of exposition are concerned, this book meets the highest standards.
International Mathematical News
- C*-Algebras. Normed Involutive Algebras. Positive Forms and Representations. The Spectrum of a C*-Algebra. Liminal C*-Algebras. The Type of a Representation. Traces and Representations. The Quasi-Spectrum. Integration and Disintegration of Representations. C*-Algebras of Type I. Continuous Fields of C*-Algebras. Extension to C*-Algebras of the Stone-Weierstrass Theorem. The Enveloping von Neumann Algebra of a C*-Algebra. Applications to Group Representations. Unitary Representations of Locally Compact Groups. Square-Integrable Irreducible Representations. Representations of Compact Groups. Almost-Periodic Functions. Characters of a Locally-Compact Group. The Dual of a Locally-Compact Group. Appendices. References.