Loomis--Sikorski Theorem and Stone Duality for Effect Algebras with Internal State

2010/06/02 by Buhagiar, D., Chetcutti, E., Dvurečenskij, A.
#03G12 #46C15 #81P10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1006.0503

Abstract

Recently Flaminio and Montagna, \citeFlMo, extended the language of MV-algebras by adding a unary operation, called a state-operator. This notion is introduced here also for effect algebras. Having it, we generalize the Loomis--Sikorski Theorem for monotone σ-complete effect algebras with internal state. In addition, we show that the category of divisible state-morphism effect algebras satisfying (RDP) and countable interpolation with an order determining system of states is dual to the category of Bauer simplices Ω such that ∂_e Ω is an F-space.

Related

• Stone Duality Type Theorems for MV-algebras with Internal State
• State BL-algebras
• States of finite effect algebras
• Effect algebras with state operator
• State morphism MV-algebras