Effect algebras with state operator

TL;DR

This paper investigates state operators on convex effect algebras, exploring their connections with conditional expectations and probability measures in algebraic frameworks like JC-algebras and MV-algebras.

Contribution

It introduces a comprehensive study of state operators on convex effect algebras and relates them to conditional expectations and probabilistic structures.

Findings

State operators are characterized on convex effect algebras.

Connections between state operators and conditional expectations are established.

Applications to effect algebras of unital JC- and JW-algebras are demonstrated.

Abstract

State operators on convex effect algebras, in particular effect algebras of unital JC-algebras, JW-algebras and convex sigma-MV algebras are studied and their relations with conditional expectations in algebraic sense as well as in the sense of probability on MV-algebras are shown.