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arXiv · 0806.3635

A reduction method for noncommutative $L_p$-spaces and applications

Uffe Haagerup·Marius Junge·Quanhua Xu
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Abstract

We consider the reduction of problems on general noncommutative $L_p$-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is a unpublished result of the first named author which approximates any noncommutative $L_p$-space by tracial ones. We show that under some natural conditions a map between two von Neumann algebras extends to their crossed products by a locally compact abelian group or to their noncommutative $L_p$-spaces. We present applications of these results to the theory of noncommutative martingale inequalities by reducing most recent general noncommutative martingale/ergodic inequalities to those in the tracial case.

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Uffe Haagerup, Marius Junge, Quanhua Xu. 2009-09-01. A reduction method for noncommutative $L_p$-spaces and applications. https://arxiv.org/abs/0806.3635

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