By V.S. Sunder

Why This publication: the idea of von Neumann algebras has been transforming into in leaps and boundaries within the final twenty years. It has continuously had robust connections with ergodic conception and mathematical physics. it really is now commencing to make touch with different parts similar to differential geometry and K-Theory. There appears a powerful case for placing jointly a publication which (a) introduces a reader to a couple of the elemental idea had to take pleasure in the hot advances, with no getting slowed down by way of an excessive amount of technical element; (b) makes minimum assumptions at the reader's history; and (c) is sufficiently small in dimension not to try out the stamina and endurance of the reader. This ebook attempts to satisfy those requisites. at the least, it's only what its name broadcasts it to be -- a call for participation to the interesting international of von Neumann algebras. it's was hoping that once perusing this publication, the reader will be tempted to fill within the a number of (and technically, capacious) gaps during this exposition, and to delve additional into the depths of the idea. For the professional, it suffices to say the following that once a few preliminaries, the publication commences with the Murray - von Neumann type of things, proceeds in the course of the uncomplicated modular thought to the III). type 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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G ) d e n o t e the Hilbert spaceof square-summablefunctions on G: <-]. ,r"li(r)12 There is a canonical orthonormalbasis{8,: t e G')of P(G), where ! 2 ( G=) [ r ' o - o : pue) srolceJ elrurJur 3o fpnls orll JoJ lool InJJa^\od e septrrord qclq^\ 'ruaroaql r{€se{BJ-BlruroI palerqoleJ oql ,(q pelerlsuoluep , t l E u r c u . lolce; flrressocou B uo el€ls lururou lnJr{lleJ e sl 0 teql 'ueql 'esoclclns lou) 'I(c)t'z'z oldruexg 'Jcl salEls Ierurou InJrllr€J IBrelas llrup€ soop (aceds ' : a r r a m o 1 1' l e u o l l r u n J l r a q l l H a l q e r e d a sr u o E u r l e r a d o ) r o l c e g f r a r r a € qcns llurp€ lou soop rolJ€J ellulJul u?

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