Contemporary Mathematics 1994; 399 pp; softcover Volume: 167 ISBN10: 0821851756 ISBN13: 9780821851753 List Price: US$79 Member Price: US$63.20 Order Code: CONM/167
 This volume contains the proceedings of an AMS Special Session held at the Joint Mathematics Meetings in San Antonio in January 1993 to celebrate the first fifty years of \(C^*\)algebra theory. The book contains carefully written expository and research articles by leaders in the field. Also included is a reprinting of the original 1943 paper on \(C^*\)algebras by Gelfand and Neumark, which has had such a profound influence on the field. The volume covers a broad spectrum of topics, including the GelfandNeumark theorems, \(C^*\)algebras and quantization, projections in \(C^*\)algebras, Mackey's theory of group representations and their relation to \(C^*\)algebras, transformation group \(C^*\)algebras, the influence of algebraic topology on \(C^*\)algebras, Ktheory and index theory in operator algebras, exponential rank in \(C^*\)algebras, and a survey of the development of type III von Neumann algebras. With historical perspectives and uptodate overviews to orient readers new to the field, this book will interest mathematicians, physicists, and mathematical historians. Readership Advanced graduate students, professional mathematicians and physicists. Reviews "The articles are of an impressively high standard and wideranging in their scope ... best picture of the subject since the Proceedings of the 1980 Kingston Symposium. All operator algebraists will want a copy of this book on their shelves, as will workers in those areas of mathematics and physics where \(C^*\)algebra theory has an influence. The editor ... is to be highly congratulated on a highly successful enterprise."  Bulletin of the London Mathematical Society Table of Contents  I. M. Gelfand and M. A. Neumark  On the imbedding of normed rings into the ring of operators in Hilbert space
 R. V. Kadison  Notes on the GelfandNeumark theorem
 I. E. Segal  \(C^\ast\)algebras and quantization
 M. A. Rieffel  Quantization and \(C^\ast\)algebras
 E. G. Effros  Some quantizations and reflections inspired by the GelfandNaimark theorem
 W. B. Arveson  The role of \(C^\ast\)algebras in infinite dimensional numerical linear algebra
 B. Blackadar  Projections in \(C^\ast\)algebras
 J. Rosenberg  \(C^\ast\)algebras and Mackey's theory of group representations
 J. Packer  Transformation group \(C^\ast\)algebras: A selective survey
 C. Schochet  Algebraic topology and \(C^\ast\)algebras
 M. Takesaki  Twentyfive years in the theory of type III von Neumann algebras
 P. Baum, A. Connes, and N. Higson  Classifying space for proper actions and \(K\)theory of group \(C^\ast\)algebras
 R. G. Douglas  Odd index theorems and operator algebras
 H. Moscovici and F. Wu  Index theory without symbols
 N. C. Phillips  A survey of exponential rank
 Appendix
 I. Gelfand and M. Neumark  On the imbedding of normed rings into the ring of operators in Hilbert space
