By V.S. Sunder
Why This booklet: the idea of von Neumann algebras has been starting to be in leaps and boundaries within the final two decades. It has constantly had powerful connections with ergodic concept and mathematical physics. it truly is now starting to make touch with different parts corresponding to differential geometry and K-Theory. There appears to be like a robust case for placing jointly a ebook which (a) introduces a reader to a few of the elemental concept had to take pleasure in the new advances, with out getting slowed down through an excessive amount of technical element; (b) makes minimum assumptions at the reader's heritage; and (c) is sufficiently small in measurement not to try out the stamina and persistence of the reader. This booklet attempts to fulfill those necessities. as a minimum, it's only what its name publicizes it to be -- a call for participation to the intriguing global of von Neumann algebras. it's was hoping that once perusing this ebook, the reader can be tempted to fill within the quite a few (and technically, capacious) gaps during this exposition, and to delve extra into the depths of the speculation. For the specialist, it suffices to say the following that once a few preliminaries, the publication commences with the Murray - von Neumann type of things, proceeds during the uncomplicated modular idea to the III). class of Connes, and concludes with a dialogue of crossed-products, Krieger's ratio set, examples of things, and Takesaki's duality theorem.
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