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.
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978-0-8218-5175-3 (9780821851753)
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Schweitzer Klassifikation
On the imbedding of normed rings into the ring of operators in Hilbert space by I. M. Gelfand and M. A. Neumark Notes on the Gelfand-Neumark theorem by R. V. Kadison $C^\ast$-algebras and quantization by I. E. Segal Quantization and $C^\ast$-algebras by M. A. Rieffel Some quantizations and reflections inspired by the Gelfand-Naimark theorem by E. G. Effros The role of $C^\ast$-algebras in infinite dimensional numerical linear algebra by W. B. Arveson Projections in $C^\ast$-algebras by B. Blackadar $C^\ast$-algebras and Mackey's theory of group representations by J. Rosenberg Transformation group $C^\ast$-algebras: A selective survey by J. Packer Algebraic topology and $C^\ast$-algebras by C. Schochet Twenty-five years in the theory of type III von Neumann algebras by M. Takesaki Classifying space for proper actions and $K$-theory of group $C^\ast$-algebras by P. Baum, A. Connes, and N. Higson Odd index theorems and operator algebras by R. G. Douglas Index theory without symbols by H. Moscovici and F. Wu A survey of exponential rank by N. C. Phillips Appendix On the imbedding of normed rings into the ring of operators in Hilbert space by I. Gelfand and M. Neumark.
