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Are there any good introductory type of books that contain dilation theories of Sz-Nagy, Rohlin and Akcoglu?

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Could you try to narrow down what you are looking for? I am aware of the Nagy dilation theorem but I don't really know what "dilation theory of Nagy" is supposed to be –  Yemon Choi Sep 1 '13 at 2:58
    
Yes, that's the one I was referring to: Sz-Nagy dilation. –  user39401 Sep 9 '13 at 23:16

2 Answers 2

The following very readable book should be of interest to you:

V. Paulsen. "Completely bounded maps and operator algebras". Cambridge University Press (2003).

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Apart from Paulsen's book on completely bounded maps you may find Harmonic Analysis of Operators on Hilbert Space by Sz.-Nagy, C. Foias, H. Bercovici & L. Kérchy interesting. It should cover most of Sz.-Nagy's work.

A nice exposition of the the Akcoglu-Sucheston dilation theorem (with full proofs) can be found in G. Fendler's lecture notes On Dilations and Transference for Continuous One-Parameter Semigroups of Positive Contractions on Lp-spaces

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