Some properties of D-weak operator topology
Marcel PolakoviΔ Β· Mathematica Slovaca Β· 2020
Abstract Let π D (π) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space π. The D-weak operator topology (introduced by other authors) on π D (π) is investigated. The corresponding closure of the set of bounded elements of π D (π) is the whole π D (π). The closure of the set of all unbounded elements of π D (π) is also the set π D (π). If Q is arbitrary unbounded element of π D (π), it determines an interval in π D (π), 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.