States on sharply dominating effect algebras

TL;DR

This paper characterizes a class of effect algebras using a basic decomposition property and proves a state smearing theorem, advancing the mathematical understanding of these algebraic structures.

Contribution

It introduces the basic decomposition property for Archimedean sharply dominating atomic lattice effect algebras and proves the state smearing theorem for them.

Findings

Characterization of effect algebras via basic decomposition

Proof of the state smearing theorem for these algebras

Enhanced understanding of the structure of effect algebras

Abstract

We prove that Archimedean sharply dominating atomic lattice effect algebras can be characterized by property called basic decomposition of elements. As an application we prove the state smearing theorem for these effect algebras.