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I am interested in non-commutative $L^p$ spaces. I have a very basic background on von Neumann algebras. But all the papers appearing now a days really requires very deep knowledge of von Neumann algebras. Also the theory of von Neumann algebras is very vast. So can anyone tell me some of the books or lecture notes on von Neumann algebras and the specific topics of von Neumann algebras which will be sufficient for me to start studying recent papers in this field? My background in Real Variable Theory is good. So I am mostly interested in Littlewood-Paley theory/ Calderon-Zygmund theory on non-commutative $L^p$ spaces.

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    $\begingroup$ Why don't you ask your adviser?? He is the best person to know what will be useful for you. $\endgroup$
    – abx
    Commented May 17, 2017 at 8:32
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    $\begingroup$ See mathoverflow.net/questions/236853/… for books on non-commutative $L^p$ spaces in particular. $\endgroup$
    – Nate Eldredge
    Commented May 17, 2017 at 13:28
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    $\begingroup$ Takesaki, volumes 1 and 2. $\endgroup$
    – Nik Weaver
    Commented May 17, 2017 at 14:11
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    $\begingroup$ And honestly, I don't see why this question was put on hold. $\endgroup$
    – Nik Weaver
    Commented May 17, 2017 at 14:12
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    $\begingroup$ Yamagami's paper "Algebraic aspects in modular theory" does a really good job explaining noncommutative L^p-spaces and related topics like Tomita-Takesaki theory, highly recommended. $\endgroup$
    – Dmitri Pavlov
    Commented May 18, 2017 at 8:45

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