An operator-valued Lyapunov theorem

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dc.contributor.authorPlosker, Sarah
dc.contributor.authorRamsey, Christopher
dc.date.accessioned2020-12-17
dc.date.accessioned2022-05-31T01:43:00Z
dc.date.available2022-05-31T01:43:00Z
dc.date.issued2019
dc.description.abstractWe generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of quantum effects (positive operators bounded above by the identity operator) under a sufficient condition on the non-injectivity of integration. To prove the operator-valued version of Lyapunov's theorem, we must first define the notions of essentially bounded, essential support, and essential range for quantum random variables (Borel measurable functions from a set to the bounded linear operators acting on a Hilbert space).
dc.format.extent276.58KB
dc.format.mimetypePDF
dc.identifier.citationPlosker, S., & Ramsey, C. (2019). An operator-valued Lyapunov theorem. Journal of Mathematical Analysis and Applications 469(1), 117-125. https://doi.org/10.1016/j.jmaa.2018.09.003
dc.identifier.doihttps://doi.org/10.1016/j.jmaa.2018.09.003
dc.identifier.urihttps://hdl.handle.net/20.500.14078/2103
dc.languageEnglish
dc.language.isoen
dc.rightsAttribution-NonCommercial-NoDerivs (CC BY-NC-ND)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectLyapunov Theorem
dc.subjectoperator valued measure
dc.subjectquantum probability measure
dc.subjectatomic and nonatomic measures
dc.titleAn operator-valued Lyapunov theorem
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