Markov Operators and $C^{*}$-Algebras

TL;DR

This paper explores the connection between Markov operators on compact spaces and their associated $C^{*}$-algebras via topological quivers, providing a new algebraic framework for analyzing probabilistic properties.

Contribution

It introduces a novel method to construct $C^{*}$-algebras from Markov operators using topological quivers, linking probabilistic and operator algebraic structures.

Findings

Constructs $C^{*}$-algebras reflecting Markov operator properties

Establishes a topological quiver framework for probabilistic analysis

Bridges probabilistic dynamics with operator algebra theory

Abstract

A Markov operator $P$ acting on $C(X)$, where $X$ is compact, gives rise to a natural topological quiver. We use the theory of such quivers to attach a $C^{*}$-algebra to $P$ in a fashion that reflects some of the probabilistic properties of $P$.