A reduction method for noncommutative $L_p$-spaces and applications
Operator Algebras
2009-09-01 v2 Functional Analysis
Abstract
We consider the reduction of problems on general noncommutative -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 The main tool is a unpublished result of the first named author which approximates any noncommutative -space by tracial ones.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 -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.
Cite
@article{arxiv.0806.3635,
title = {A reduction method for noncommutative $L_p$-spaces and applications},
author = {Uffe Haagerup and Marius Junge and Quanhua Xu},
journal= {arXiv preprint arXiv:0806.3635},
year = {2009}
}