جبر C*: جشن پنجاه ساله: جلسه ویژه Ams به یادبود پنجاه سال اول نظریه جبر C*

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. Dedication Contents Preface On the imbedding of normed rings into the ring of operators in Hilbert space • Israel M. Gelfand and Mark A. Neumark Notes on the Gelfand-Neumark theorem • Richard V. Kadison C*-algebras and quantization • Irving E. Segal Quantization and C*-algebras • Marc A. Rieffel Some quantizations and reflections inspired by the Gelfand-Naimark theorem • Edward G. Effros The role of C*-algebras in infinite dimensional numerical linear algebra • William B. Arveson Projections in C*-algebras • Bruce Blackadar C*-algebras and Mackey’s theory of group representations • Jonathan Rosenberg Transformation group C*-algebras: A selective survey • Judith Packer Algebraic topology and C*-algebras • Claude Schochet Twenty-five years in the theory of type III von Neumann algebras • Masamichi Takesaki Classifying space for proper actions and K-theory of group C*-algebras • Paul Baum, Alain Connes, and Nigel Higson Odd index theorems and operator algebras • Ronald G. Douglas Index theory without symbols • Henri Moscovici and Fangbing Wu A survey of exponential rank • N. Christopher Phillips Appendix: On the imbedding of normed rings into the ring of operators in Hilbert space • I. Gelfand and M. Neumark 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. This book covers a spectrum of topics, including the Gelfand-Neumark theorems, $C^*$-algebras and quantization and projections in $C^*$-algebras.