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The Lattice and Simplex Structure of States on Pseudo Effect Algebras

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Abstract

We study states, measures, and signed measures on pseudo effect algebras with some version of the Riesz Decomposition Property (RDP). We show that the set of all Jordan signed measures is always an Abelian Dedekind complete ℓ-group. Therefore, the state space of a pseudo effect algebra with RDP is either empty or a nonempty Choquet simplex or even a Bauer simplex. This will allow to represent states on pseudo effect algebras by standard integrals.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Correspondence to Anatolij Dvurečenskij.

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The author thanks for the support by Center of Excellence SAS—Quantum Technologies—ERDF OP R&D Projects CE QUTE ITMS 26240120009 and meta-QUTE ITMS 26240120022, the grant VEGA No. 2/0032/09 SAV.

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Dvurečenskij, A. The Lattice and Simplex Structure of States on Pseudo Effect Algebras. Int J Theor Phys 50, 2758–2775 (2011). https://doi.org/10.1007/s10773-011-0775-1

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  • DOI: https://doi.org/10.1007/s10773-011-0775-1

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