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Proceedings of the American Mathematical Society
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Proceedings of the American Mathematical Society
Article . 1992 . Peer-reviewed
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Proceedings of the American Mathematical Society
Article . 1992 . Peer-reviewed
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https://dx.doi.org/10.1090/s00...
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Finitely Additive Gleason Measures

Finitely additive Gleason measures
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1992Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 115, page 191 (issn: 0002-9939, Copyright policy )
Authors: Dvurečenskij, Anatolij;

doi: 10.2307/2159585 , 10.1090/s0002-9939-1992-1072335-9

Finitely Additive Gleason Measures

Abstract

We describe the set of all finitely additive measures which attain also infinite values on a quantum logic of a Hilbert space and which are expressible via the generalized Gleason-Lugovaja-Sherstnev formula. We prove that this set consists of those which are regular with respect to the set of all finite-dimensional subspaces. In addition, we show that this regularity does not entail the countable additivity, in general.

Keywords

finitely additive measures which attain also infinite values on a quantum logic of a Hilbert space, Free probability and free operator algebras, Noncommutative measure and integration, Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects), Noncommutative probability and statistics, Characterizations of Hilbert spaces, Measures on Boolean rings, measure algebras, generalized Gleason-Lugovaja-Sherstnev formula, Quantum logic

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
bronze