An operator-valued Lyapunov theorem
| dc.contributor.author | Plosker, Sarah | |
| dc.contributor.author | Ramsey, Christopher | |
| dc.date.accessioned | 2020-12-17 | |
| dc.date.accessioned | 2022-05-31T01:43:00Z | |
| dc.date.available | 2022-05-31T01:43:00Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | We 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.extent | 276.58KB | |
| dc.format.mimetype | ||
| dc.identifier.citation | Plosker, 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.doi | https://doi.org/10.1016/j.jmaa.2018.09.003 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14078/2103 | |
| dc.language | English | |
| dc.language.iso | en | |
| dc.rights | Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Lyapunov Theorem | |
| dc.subject | operator valued measure | |
| dc.subject | quantum probability measure | |
| dc.subject | atomic and nonatomic measures | |
| dc.title | An operator-valued Lyapunov theorem | en |
| dc.type | Article Post-Print | |
| dspace.entity.type |
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