Constrictive Markov operators induced by Markov processes

Abstract

Consider a constrictive Markov operator \(T:L^1(X, \Sigma , \mu ) \rightarrow L^1(X, \Sigma , \mu )\) defined on a finite measure space \((X, \Sigma , \mu )\). We give a necessary and sufficient condition for a constrictive Markov operator T which is an integral operator with stochastic kernel satisfying \(T\mathbf {1}_X=\mathbf {1}_X\).