On the properties of spectral effect algebras

Anna Jenčová and Martin Plávala

Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, Bratislava, Slovakia

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The aim of this paper is to show that there can be either only one or uncountably many contexts in any spectral effect algebra, answering a question posed in [S. Gudder, Convex and Sequential Effect Algebras, (2018), arXiv:1802.01265]. We also provide some results on the structure of spectral effect algebras and their state spaces and investigate the direct products and direct convex sums of spectral effect algebras. In the case of spectral effect algebras with sharply determining state space, stronger properties can be proved: the spectral decompositions are essentially unique, the algebra is sharply dominating and the set of its sharp elements is an orthomodular lattice. The article also contains a list of open questions that might provide interesting future research directions.

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Cited by

[1] Alessandro Bisio, "The importance of being spectral", Quantum Views 3, 15 (2019).

[2] Abraham Westerbaan, Bas Westerbaan, and John van de Wetering, "The three types of normal sequential effect algebras", Quantum 4, 378 (2020).

[3] Anna Jenčová and Sylvia Pulmannová, "Geometric and algebraic aspects of spectrality in order unit spaces: A comparison", Journal of Mathematical Analysis and Applications 504 1, 125360 (2021).

[4] Martin Plávala, "General probabilistic theories: An introduction", arXiv:2103.07469.

[5] Stan Gudder, "Contexts in Convex and Sequential Effect Algebras", arXiv:1901.10640.

The above citations are from Crossref's cited-by service (last updated successfully 2021-10-20 07:22:34) and SAO/NASA ADS (last updated successfully 2021-10-20 07:22:35). The list may be incomplete as not all publishers provide suitable and complete citation data.

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