Dilations and rigid factorisations on noncommutative L^p-spaces

Christian Le Merdy; Marius Junge

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Dilations and rigid factorisations on noncommutative L^p-spaces

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arxiv 0803.4410 v1 pith:Q3N7RL5P submitted 2008-03-31 math.OA math.FA

Dilations and rigid factorisations on noncommutative L^p-spaces

Marius Junge , Christian Le Merdy This is my paper

classification math.OA math.FA

keywords noncommutativep-spacesdilationpositiveakcogluanaloganalogsclassical

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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.

Dilations and rigid factorisations on noncommutative L^p-spaces

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