eBook ISBN:  9780821877586 
Product Code:  CONM/167.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821877586 
Product Code:  CONM/167.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 167; 1994; 399 ppMSC: Primary 22; 46; 58; 19; Secondary 55
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.
ReadershipAdvanced graduate students, professional mathematicians and physicists.

Table of Contents

Articles

I. Gel′fand and M. Neumark — On the imbedding of normed rings into the ring of operators in Hilbert space [ MR 1292007 ]

Richard V. Kadison — Notes on the Gel′fandNeumark theorem [ MR 1292008 ]

Irving Segal — $C^\ast $algebras and quantization [ MR 1292009 ]

Marc A. Rieffel — Quantization and $C^\ast $algebras [ MR 1292010 ]

Edward G. Effros — Some quantizations and reflections inspired by the Gel′fandNaĭmark theorem [ MR 1292011 ]

William Arveson — The role of $C^\ast $algebras in infinitedimensional numerical linear algebra [ MR 1292012 ]

Bruce Blackadar — Projections in $C^\ast $algebras [ MR 1292013 ]

Jonathan Rosenberg — $C^\ast $algebras and Mackey’s theory of group representations [ MR 1292014 ]

Judith Packer — Transformation group $C^\ast $algebras: a selective survey [ MR 1292015 ]

Claude Schochet — Algebraic topology and $C^\ast $algebras [ MR 1292016 ]

Masamichi Takesaki — Twentyfive years in the theory of type ${\rm III}$ von Neumann algebras [ MR 1292017 ]

Paul Baum, Alain Connes and Nigel Higson — Classifying space for proper actions and $K$theory of group $C^\ast $algebras [ MR 1292018 ]

R. G. Douglas — Odd index theorems and operator algebras [ MR 1292019 ]

Henri Moscovici and Fangbing Wu — Index theory without symbols [ MR 1292020 ]

N. Christopher Phillips — A survey of exponential rank [ MR 1292021 ]

I. Gelfand and M. Neumark — On the imbedding of normed rings into the ring of operators in Hilbert space


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


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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 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.
Advanced graduate students, professional mathematicians and physicists.

Articles

I. Gel′fand and M. Neumark — On the imbedding of normed rings into the ring of operators in Hilbert space [ MR 1292007 ]

Richard V. Kadison — Notes on the Gel′fandNeumark theorem [ MR 1292008 ]

Irving Segal — $C^\ast $algebras and quantization [ MR 1292009 ]

Marc A. Rieffel — Quantization and $C^\ast $algebras [ MR 1292010 ]

Edward G. Effros — Some quantizations and reflections inspired by the Gel′fandNaĭmark theorem [ MR 1292011 ]

William Arveson — The role of $C^\ast $algebras in infinitedimensional numerical linear algebra [ MR 1292012 ]

Bruce Blackadar — Projections in $C^\ast $algebras [ MR 1292013 ]

Jonathan Rosenberg — $C^\ast $algebras and Mackey’s theory of group representations [ MR 1292014 ]

Judith Packer — Transformation group $C^\ast $algebras: a selective survey [ MR 1292015 ]

Claude Schochet — Algebraic topology and $C^\ast $algebras [ MR 1292016 ]

Masamichi Takesaki — Twentyfive years in the theory of type ${\rm III}$ von Neumann algebras [ MR 1292017 ]

Paul Baum, Alain Connes and Nigel Higson — Classifying space for proper actions and $K$theory of group $C^\ast $algebras [ MR 1292018 ]

R. G. Douglas — Odd index theorems and operator algebras [ MR 1292019 ]

Henri Moscovici and Fangbing Wu — Index theory without symbols [ MR 1292020 ]

N. Christopher Phillips — A survey of exponential rank [ MR 1292021 ]

I. Gelfand and M. Neumark — On the imbedding of normed rings into the ring of operators in Hilbert space

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