Spectrality in convex sequential effect algebras

• URL: http://arxiv.org/abs/2312.13003v1
• Date: Wed, 20 Dec 2023 13:10:17 GMT
• Title: Spectrality in convex sequential effect algebras
• Authors: Anna Jen\v{c}ov\'a, Sylvia Pulmannov\'a
• Abstract summary: For convex and sequential effect algebras, we study spectrality in the sense of Foulis. We show that under additional conditions, such effect algebra is spectral if and only if every maximal commutative subalgebra is monotone $sigma$-complete.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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