C Algebras, 1943-1993: A Fifty Year Celebration

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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.

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Editorial Reviews

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Reprints the seminal 1943 paper on C*-algebras by Gelfand and Neumark, and offers 14 original papers exploring the field's subsequent development and current status. Among the topics are quantization, infinite dimensional numerical linear algebra, algebraic topology, and index theory without symbols. For true history buffs, the 1943 article is also presented in facsimile. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Preface
On the imbedding of normed rings into the ring of operators in Hilbert space 3
Notes on the Gelfand-Neumark theorem 21
C*-algebras and quantization 55
Quantization and C*-algebras 67
Some quantizations and reflections inspired by the Gelfand-Naimark theorem 99
The role of C*-algebras in infinite dimensional numerical linear algebra 115
Projections in C*-algebras 131
C*-algebras and Mackey's theory of group representations 151
Transformation group C*-algebras: A selective survey 183
Algebraic topology and C*-algebras 219
Twenty-five years in the theory of type III von Neumann algebras 233
Classifying space for proper actions and K-theory of group C*-algebras 241
Odd index theorems and operator algebras 293
Index theory without symbols 305
A survey of exponential rank 353
Appendix: On the imbedding of normed rings into the ring of operators in Hilbert space A-3
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