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I've read R Kadison, Ringrose "fundamental of operator Vol 1" and R G Douglas "Banach technique in operator algebra".I wanna know how far I'm from the Alain Connes' work. Is there any route (paper and books) leading to well-understanding of that topics?

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I would strongly recommend to have a look (and to always keep available) to the books by Takesaki "The theory of Operator algebras" I,II and III

You might not need to know everything that is in these books but they contains most of the tools involved in the classifications, and even some part of the classification (all the basics of Von neuman algebra theory, tomita-Takesaki theory, Connes cocycle, injective = AFD etc...).

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  • $\begingroup$ Thank you for your answer. About the books you recommened,would it be possible to understand some later chapters without reading all the previous chapters? $\endgroup$
    – Jack
    Jun 1 '17 at 0:55
  • $\begingroup$ Yes of course. I wouldn't recommand to read them from the first page to the last any way. $\endgroup$ Jun 27 '17 at 7:10
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I guess i am in the same wavelenght as you are..and i am trying to read lecture notes on noncommutative geometry and quantum groups (just google)..also nigel higson's analytic k homology...the first book is pretty good for beginner like me and ..may be you as well!

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