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

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

2010-06-02

arxiv.org/abs/1006.0503v1

Mathematics

Functional Analysis

Scientific paper

Recently Flaminio and Montagna, \cite{FlMo}, 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 $\sigma$-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 $\Omega$ such that $\partial_e \Omega$ is an F-space.

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