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- W2020111478 abstract "Let documentclass[12pt]{minimal}begin{document}$S(mathcal {H})$end{document}S(H) be the set of all bounded self-adjoint linear operators on a complex Hilbert space documentclass[12pt]{minimal}begin{document}$mathcal {H}.$end{document}H. In 2006, Gudder [Math. Slovaca 56, 573 (2006)] introduced a new order ≼ on documentclass[12pt]{minimal}begin{document}$S(mathcal {H}).$end{document}S(H). Since then, the existence conditions and representations of the supremum and infimum of two elements in documentclass[12pt]{minimal}begin{document}$S(mathcal {H})$end{document}S(H) with respect to the order ≼ have been intensively studied. Specifically, Li and Sun [J. Math. Phys. 50, 122107 (2009)]10.1063/1.3272542 obtained simpler representations of A ∧ P and A ∨ P, where documentclass[12pt]{minimal}begin{document}$Ain S(mathcal {H})$end{document}A∈S(H) and P is an orthogonal projection on documentclass[12pt]{minimal}begin{document}$mathcal {H}.$end{document}H. In this note, we present more intuitive and concise results on A ∨ P and extend the results of Li and Sun to more general cases. Moreover, some applications of our results are given to show that our results are easier to deal with." @default.
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- W2020111478 date "2011-12-01" @default.
- W2020111478 modified "2023-09-26" @default.
- W2020111478 title "On the supremum and infimum of bounded quantum observables" @default.
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- W2020111478 doi "https://doi.org/10.1063/1.3671331" @default.
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