Sequences of Operators, Monotone in the Sense of Contractive Domination - Hassi, S.; de Snoo, H. S. V. (Springer Nature, 2024)
A sequence of operators Tn from a Hilbert space H to Hilbert spaces Kn which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator T from H to a Hilbert space K. Moreover, the closability or closedness of Tn is preserved in the limit. The closures converge likewise and the connection between the limits is investigated. There is no similar way of dealing directly with linear relations. However, the sequence of closures is still nondecreasing and then the convergence is governed by the monotonicity principle. There are some related results for nonincreasing sequences.
Keywords: Domination of linear relations; Monotonicity principle; Nondecreasing sequences of linear relations in the sense of domination; fi=Matematiikka|en=Mathematics|