Spectrality in convex sequential effect algebras

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.

arXiv comment18 pages. arXiv admin note: text overlap with arXiv:2111.02166

References in corpus (10)

• Informational derivation of Quantum Theory
• Quantum Theory From Five Reasonable Axioms
• Position Dependent Mass Oscillators and Coherent States
• An effect-theoretic reconstruction of quantum theory
• Compression Bases in Unital Groups
• On the properties of spectral effect algebras
• A characterisation of ordered abstract probabilities
• Geometric and algebraic aspects of spectrality in order unit spaces: a comparison
• Spectral resolutions in effect algebras
• Handelman's theorem for an order unit normed space