A reduction method for noncommutative L_p-spaces and applications

By Uffe Haagerup, Marius Junge, Quanhua Xu. 2008

115 citations recorded by the source corpus.

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 The main tool is an unpublished result of the first-named author which approximates any noncommutative L p -space by tracial ones.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

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a2c6d3a13c55ce26f3702a09347b87865c6b1074

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. 'Eric Ricard
2. D. Potapov
3. Quanhua Xu
4. Fedor Sukochev
5. Nathanial P. Brown Narutaka Ozawa
6. Alan L. Carey

In Mathematical Physics

1. D. Potapov
2. Sjoerd Dirksen
3. Fedor Sukochev
4. B. Pagter
5. Quanhua Xu
6. 'Eric Ricard
7. Marius Junge
8. Javier Parcet

Citations in the corpus

• Rosenthal inequalities in noncommutative symmetric spaces (2011, methodology): “We refer to [14, 18] for more details on Haagerup L-spaces.”
• A noncommutative martingale convexity inequality (2014, methodology): “Using the Haagerup reduction theorem as in [7], one can reduce both theorems to the finite case.”