Weak Markov Operators

TL;DR

This paper introduces and characterizes weak Markov operators, a generalization of Markov operators in f-algebras, focusing on their extreme points and properties.

Contribution

It provides a characterization of the extreme points of weak Markov operators, extending the classical theory to weak order units.

Findings

Characterization of extreme points of weak Markov operators

Extension of Markov operator theory to weak order units

New insights into the structure of 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.