Ornstein and Sucheston first proved that for a given positive contraction there exists such that if , then . This result was referred to as the zero-two law. In the present article, we prove a generalized uniform zero-two law for the multiparametric family of positive contractions of noncommutative -spaces. Moreover, we also establish a vector-valued analogue of the uniform zero-two law for positive contractions of —the noncommutative -spaces associated with center-valued traces.
"On a generalized uniform zero-two law for positive contractions of noncommutative -spaces and its vector-valued extension." Banach J. Math. Anal. 12 (3) 600 - 616, July 2018. https://doi.org/10.1215/17358787-2017-0054