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I have some -possibly- simple but broad questions: Where to begin the study of von Neumann Algebras? Which are the important questions in the field that guide current research? I'm interested in learning the basics to start working at research level in the field.

My backgroud is: some basic Functional and Real Analysis (e.g. the material covered in Gerald Teschl Topics in Real...), some Point Set and Algebraic Topology (e.g. Munkres), some Algebra (e.g. Lang's Algebra), some basic Operator Algebras (chapters 4 and 5 of Kadison & Ringrose).

Thanks.

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    $\begingroup$ start with Lectures on von Neumann Algebras by S. Stratila $\endgroup$
    – SiOn
    Commented Apr 13, 2014 at 22:16
  • $\begingroup$ Not an expert, but I'd say Takesaki vol. 2 is a good place to start. $\endgroup$
    – Nik Weaver
    Commented Apr 13, 2014 at 23:49

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For a rapid introduction see http://www.math.berkeley.edu/~vfr/MATH20909/VonNeumann2009.pdf (Von Neumann Algebras, by Vaughan F.R. Jones -- "The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. ")

A survey "Von Neumann Algebras in Mathematics and Physics" by the same author would be also helpful for a broad perspective: http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0121.0138.ocr.pdf

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