Completely order bounded maps on non-commutative L-p-spaces

摘要

We define norms on L-p(M) circle times M-n where M is a von Neumann algebra and M-n is the space of complex n x n matrices. We show that a linear map T : L-p(M) -> L-q(N) is decomposable if N is an injective von Neumann algebra, the maps T circle times IdM(n) have a common upper bound with respect to our defined norms, and p = infinity or q = 1. For 2p