By V.S. Sunder

Why This booklet: the speculation of von Neumann algebras has been turning out to be in leaps and limits within the final two decades. It has constantly had powerful connections with ergodic concept and mathematical physics. it truly is now commencing to make touch with different components similar to differential geometry and K-Theory. There seems a robust case for placing jointly a e-book which (a) introduces a reader to a couple of the elemental concept had to have fun with the hot advances, with out getting slowed down via 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 the stamina and persistence of the reader. This e-book attempts to satisfy those specifications. at least, it's only what its name declares it to be -- a call for participation to the interesting international of von Neumann algebras. it's was hoping that when perusing this booklet, the reader may be tempted to fill within the various (and technically, capacious) gaps during this exposition, and to delve additional into the depths of the speculation. For the professional, it suffices to say right here that once a few preliminaries, the publication commences with the Murray - von Neumann category of things, proceeds throughout the simple modular concept to the III). category of Connes, and concludes with a dialogue of crossed-products, Krieger's ratio set, examples of things, and Takesaki's duality theorem.