On the properties of spectral effect algebras. (arXiv:1811.12407v2 [quant-ph] UPDATED)

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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