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- W2906198736 abstract "The paper mainly deals with suprema and infima of self-adjoint operators in a von Neumann algebra $mathcal{M}$ with respect to the spectral order. Let $mathcal{M}_{sa}$ be the self-adjoint part of $mathcal{M}$ and let $preceq$ be the spectral order on $mathcal{M}_{sa}$. We show that a decreasing net in $(mathcal{M}_{sa},preceq)$ with a lower bound has the infimum equal to the strong operator limit. The similar statement is proved for increasing net bounded above in $(mathcal{M}_{sa},preceq)$. This version of Vigier's theorem for the spectral order is used to describe suprema and infima of nonempty bounded sets of self-adjoint operators in terms of the strong operator limit and operator means. As an application of our results on suprema and infima, we study the order topology on $mathcal{M}_{sa}$ with respect to the spectral order. We show that it is finer than the restriction of the Mackey topology." @default.
- W2906198736 created "2019-01-01" @default.
- W2906198736 creator A5015348629 @default.
- W2906198736 date "2018-12-23" @default.
- W2906198736 modified "2023-09-26" @default.
- W2906198736 title "Vigier's theorem for the spectral order and its applications" @default.
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