On dominant contractions and a generalization of the zero-two law

Abstract

Zaharopol proved the following result: let $T,S:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m)$ be two positive contractions such that $T\le S$. If $\Vert S-T\Vert <1$ then $\Vert S^n-T^n\Vert <1$ for all $n\in\bn$. In the present paper we generalize this result to multi-parameter contractions acting on $L^1$. As an application of that result we prove a generalization of the "zero-two" law.

10 pages

References in corpus (1)

• A Note on Dominant Contractions of Jordan Algebras