Spectrality in convex sequential effect algebras
Quantum Physics
2023-12-21 v1 Functional Analysis
Rings and 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 -complete. Two previous results on existence of spectral resolutions in this setting are shown to require stronger assumptions.
Keywords
Cite
@article{arxiv.2312.13003,
title = {Spectrality in convex sequential effect algebras},
author = {Anna Jenčová and Sylvia Pulmannová},
journal= {arXiv preprint arXiv:2312.13003},
year = {2023}
}
Comments
18 pages. arXiv admin note: text overlap with arXiv:2111.02166