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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