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Spectrality in convex sequential effect algebras
Published 20 Dec 2023 in quant-ph, math.FA, and math.RA | (2312.13003v1)
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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