Abstract
We consider the reduction of problems on general noncommuta- tive L p-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is an unpublished result of the first-named author which approximates any noncommutative Lp-space by tracial ones.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 Lp-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.
Original language | English (US) |
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Pages (from-to) | 2125-2165 |
Number of pages | 41 |
Journal | Transactions of the American Mathematical Society |
Volume | 362 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2010 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics