Dilations and rigid factorisations on noncommutative L^p-spaces

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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.
To be published in Journal of Functional Analysis

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Operator Algebras, Functional Analysis, 46L07, 46L51, 48B28

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http://salesiana.dossiersoluciones.com/handle/123456789/157775

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.4410
 http://arxiv.org/abs/0803.4410

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arXiv