Von Neumann Algebras (North-Holland Mathematical Library) - ISBN:0444863087

Von Neumann Algebras (North-Holland Mathematical Library)

Date: 05 June 2011, 01:30

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In his introduction to the companion volume on C*-algebras, J. Dixmier makes the comment that at the time when he wrote this book, the major part of the theory of von Neumann algebras seemed to him to have reached a more or less definitive form. His belief is vindicated by the fact that during the twelve years which elapsed between the preparation of the first and second editions of the book, few major developments took place. By the time the second edition appeared in 1969, however, it was already clear that fundamental new advances had been made in the theory, and the following half-dozen years brought a succession of important results which carried the theory of von Neumann algebras to an altogether new level of richness and interest. Now, twelve years after the appearance of the second edition, the theory again seems to have reached a period of stability and it is possible to view in perspective these advances in the theory, due principally to Tomita, Takesaki and Connes, and to see how they develop and illumine the basic theory as presented in this book.

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