This is an announcement for the paper "Dilations and rigid factorisations on noncommutative L^p-spaces" by Marius Junge and Christian Le Merdy.

Abstract: We study some factorisation and dilation properties of completely positive maps on noncommutative L^p-spaces. We show that Akcoglu's dilation theorem for positive contractions on classical (=commutative) L^p-spaces has no reasonable analog in the noncommutative setting. Our study relies on non symmetric analogs of Pisier's operator space valued noncommutative L^p-spaces that we investigate in the first part of the paper.

Archive classification: math.FA math.OA

Mathematics Subject Classification: 46L07, 46L51, 48B28

Remarks: To be published in Journal of Functional Analysis

The source file(s), JLRevised.tex: 91495 bytes, is(are) stored in gzipped form as 0803.4410.gz with size 26kb. The corresponding postcript file has gzipped size 178kb.

Submitted from: clemerdy@univ-fcomte.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0803.4410

or

http://arXiv.org/abs/0803.4410

or by email in unzipped form by transmitting an empty message with subject line

uget 0803.4410

or in gzipped form by using subject line

get 0803.4410

to: math@arXiv.org.