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arXiv · 2312.13003

Spectrality in convex sequential effect algebras

Anna Jenčová·Sylvia Pulmannová
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Abstract

For convex and sequential effect algebras, we study spectrality in the sense of Foulis. We show that under additional conditions (strong archimedeanity, closedness in norm and a certain monotonicity property of the sequential product), such effect algebra is spectral if and only if every maximal commutative subalgebra is monotone $\sigma$-complete. Two previous results on existence of spectral resolutions in this setting are shown to require stronger assumptions.

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Anna Jenčová, Sylvia Pulmannová. 2023-12-20. Spectrality in convex sequential effect algebras. https://doi.org/10.1007/s10773-023-05431-8

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