Weak Markov Operators

Abstract

Let $A$ and $B$ be $f$-algebras with unit elements $e_{A}$ and $e_{B}$
respectively. A positive operator $T$ from $A$ to $B$ satisfying $T\left(
e_{A}\right) =e_{B}$ is called a Markov operator. In this definition we
replace unit elements with weak order units and, in this case, call $T$ to
be a weak Markov operator. In this paper, we characterize extreme points of
the weak Markov operators.