# Loomis-Sikorski Theorem and Stone Duality for Effect Algebras with Internal State - Mathematics > Functional Analysis

Loomis-Sikorski Theorem and Stone Duality for Effect Algebras with Internal State - Mathematics > Functional Analysis - Download this document for free, or read online. Document in PDF available to download.

Abstract: Recently Flaminio and Montagna, \cite{FlMo}, extended the language ofMV-algebras by adding a unary operation, called a state-operator. This notionis introduced here also for effect algebras. Having it, we generalize theLoomis-Sikorski Theorem for monotone $\sigma$-complete effect algebras withinternal state. In addition, we show that the category of divisiblestate-morphism effect algebras satisfying RDP and countable interpolationwith an order determining system of states is dual to the category of Bauersimplices $\Omega$ such that $\partial e \Omega$ is an F-space.

Author: D. Buhagiar, E. Chetcutti, A. Dvurečenskij

Source: https://arxiv.org/