Weak Markov Operators

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.