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$$C^*$$-Algebras: 1943-1993
Edited by: Robert S. Doran
 SEARCH THIS BOOK:
Contemporary Mathematics
1994; 399 pp; softcover
Volume: 167
ISBN-10: 0-8218-5175-6
ISBN-13: 978-0-8218-5175-3
List Price: US$83 Member Price: US$66.40
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 Gelfand-Neumark 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, K-theory 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 up-to-date overviews to orient readers new to the field, this book will interest mathematicians, physicists, and mathematical historians.

Reviews

"The articles are of an impressively high standard and wide-ranging 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

• 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 Gelfand-Neumark 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 Gelfand-Naimark 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 -- Twenty-five 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