On a generalized uniform zero-two law for positive contractions of noncommutative $L_{1}$ -spaces and its vector-valued extension

Abstract

First, Ornstein and Sucheston proved that for a given positive contrac-Such a result was labeled as "zero-two" law. In the present paper, we prove a generalized uniform "zero-two" law for multi-parametric family of positive contractions of the non-commutative L1-spaces. Moreover, we also establish a vector-valued analogous of the uniform "zero-two" law for positive contractions of L1(M, Φ)-the noncommutative L1-spaces associated with center valued trace.