On stability properties of positive contractions of $L^1$-spaces accosiated with finite von Neumann algebras

TL;DR

This paper extends the concept of the Dobrushin coefficient to positive contractions on $L^1$-spaces linked with finite von Neumann algebras and uses it to establish stability results for these contractions.

Contribution

It introduces a generalized Dobrushin coefficient for $L^1$-contractions in the context of finite von Neumann algebras and proves related stability theorems.

Findings

Extended Dobrushin coefficient to new setting

Proved stability results for $L^1$-contractions

Enhanced understanding of ergodic properties in von Neumann algebra contexts

Abstract

In the paper we extent the notion of Dobrushin coefficient of ergodicity for positive contractions defined on $L^1$-space associated with finite von Neumann algebra, and in terms of this coefficient we prove stability results for $L^1$-contractions.