Noncommutative Boyd interpolation theorems
Functional Analysis
2013-06-11 v2 Operator Algebras
Probability
Abstract
We present a new, elementary proof of Boyd's interpolation theorem. Our approach naturally yields a noncommutative version of this result and even allows for the interpolation of certain operators on l^1-valued noncommutative symmetric spaces. By duality we may interpolate several well-known noncommutative maximal inequalities. In particular we obtain a version of Doob's maximal inequality and the dual Doob inequality for noncommutative symmetric spaces. We apply our results to prove the Burkholder-Davis-Gundy and Burkholder-Rosenthal inequalities for noncommutative martingales in these spaces.
Keywords
Cite
@article{arxiv.1203.1653,
title = {Noncommutative Boyd interpolation theorems},
author = {Sjoerd Dirksen},
journal= {arXiv preprint arXiv:1203.1653},
year = {2013}
}
Comments
Reviewer's comments incorporated in this version. Title slightly changed. To appear in Trans. Amer. Math. Soc