This is an announcement for the paper "Noncommutative and vector-valued Boyd interpolation theorems" by Sjoerd Dirksen.
Abstract: We present a new, elementary proof of Boyd's interpolation theorem. Our approach naturally yields a vector-valued as well as 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.
Archive classification: math.FA math.OA math.PR
Submitted from: sjoerd.dirksen@hcm.uni-bonn.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.1653
or