Facebook Instagram Twitter RSS Feed PodBean Back to top on side

Some properties of $D$-weak operator topology

In: Mathematica Slovaca, vol. 70, no. 3
Marcel Polakovič
Detaily:
Rok, strany: 2020, 753 - 758
Kľúčové slová:
Hilbert space, generalized effect algebra, D-weak operator topology, closure
O článku:
Let $\mathcal{G}D(\mathcal{H})$ denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace $D$ of a Hilbert space $H$. The $D$-weak operator topology (introduced by other authors) on $GD(H)$ is investigated. The corresponding closure of the set of bounded elements of $GD(H)$ is the whole $GD(H)$. The closure of the set of all unbounded elements of $GD(H)$ is also the set $GD(H)$. If $Q$ is arbitrary unbounded element of $GD(H)$, it determines an interval in $GD(H)$, consisting of all operators between 0 and $Q$ (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the $D$-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.
Ako citovať:
ISO 690:
Polakovič, M. 2020. Some properties of $D$-weak operator topology. In Mathematica Slovaca, vol. 70, no.3, pp. 753-758. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0388

APA:
Polakovič, M. (2020). Some properties of $D$-weak operator topology. Mathematica Slovaca, 70(3), 753-758. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0388
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 23. 5. 2020