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\(C^*\)-Algebras: 1943-1993
Edited by: Robert S. Doran
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Contemporary Mathematics
1994; 399 pp; softcover
Volume: 167
ISBN-10: 0-8218-5175-6
ISBN-13: 978-0-8218-5175-3
List Price: US$79
Member Price: US$63.20
Order Code: CONM/167
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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.

Readership

Advanced graduate students, professional mathematicians and physicists.

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

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 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
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