Dilations and rigid factorisations on noncommutative L-P-spaces

摘要

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 nonsymmetric analogs of Pisier's operator space valued noncommutative L-p-spaces that we investigate in the first part of the paper. (c) 2007 Elsevier Inc. All rights reserved.