ON A MULTI-PARAMETRIC GENERALIZATION OF THE UNIFORM ZERO-TWO LAW IN L¹-SPACES

Abstract

Abstract. Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform "zero-two" law: let T :There are many papers devoted to generalizations of this law. In the present paper we provide a multi-parametric generalization of the uniform zero-two law for L 1 -contractions.

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

“…The aim of this paper is to prove a non-commutative version of a generalized uniform "zero-two" law for multi-parametric family of positive contractions of L 1 -spaces associated with von Neumann algebras. As a particular case (when the algebra is commutative), we recover the results of [30,31]. Moreover, we emphasize that Theorem 1.2 will be included in the main result as a particular case.…”

“…Our main result extents it for more general multiparametric contractions. We point out that if the algebra becomes commutative, then the proved theorems cover main results of [31].…”