A reduction method for non-commutative L_p-spaces and applications.

TY - JOUR

T1 - A reduction method for non-commutative L_p-spaces and applications.

AU - Haagerup, Uffe

AU - Junge, Marius

AU - Xu, Quanhua

PY - 2010/4

Y1 - 2010/4

N2 - 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 The main tool is an unpublished result of the first-named author which approximates any noncommutative Lp-space by tracial ones.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.

AB - 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 The main tool is an unpublished result of the first-named author which approximates any noncommutative Lp-space by tracial ones.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.

M3 - Journal article

SN - 0002-9947

VL - 362

SP - 2125

EP - 2165

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -