Dilations and rigid factorisations on noncommutative L^p-spaces

Details Dilations and rigid factorisations on noncommutative L^p-spaces Dilations and rigid factorisations on noncommutative L^p-spaces

2008-03-31

arxiv.org/abs/0803.4410v1

Mathematics

Operator Algebras

To be published in Journal of Functional Analysis

Scientific paper

We study some factorisation and dilation properties of completely positive maps on noncommutative L^p-spaces. We show that Akcoglu's dilation theorem for positive contractions on classical (=commutative) L^p-spaces has no reasonable analog in the noncommutative setting. Our study relies on non symmetric analogs of Pisier's operator space valued noncommutative L^p-spaces that we investigate in the first part of the paper.

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