凸序列效应代数的谱性

IF 1.3 4区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

International Journal of Theoretical Physics Pub Date : 2023-08-25 DOI:10.1007/s10773-023-05431-8

Anna Jenčová, Sylvia Pulmannová

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引用次数: 0

摘要

对于凸效应代数和序列效应代数，我们研究了傅里叶意义上的谱性。证明了在附加条件下(强阿基米德性、范数闭合性和序列积的一定单调性)，当且仅当每个极大交换子代数都是单调\(\sigma \) -完全时，这种效应代数是谱的。在这种情况下，先前关于光谱分辨率存在的两个结果表明需要更强的假设。

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Spectrality in Convex Sequential Effect Algebras

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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来源期刊

International Journal of Theoretical Physics 物理-物理：综合

CiteScore

2.50

自引率

21.40%

发文量

258

审稿时长

3.3 months

期刊介绍： International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.