Sequences of operators, monotone in the sense of contractive domination

Autor:	Hassi, Seppo, de Snoo, Henk
Rok vydání:	2023
Předmět:	Mathematics - Functional Analysis Primary 47A30 47A63 47B02 Secondary 47B25 47B65
Druh dokumentu:	Working Paper
Popis:	A sequence of operators $T_n$ from a Hilbert space ${\mathfrak H}$ to Hilbert spaces ${\mathfrak K}_n$ which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator $T$ from ${\mathfrak H}$ to a Hilbert space ${\mathfrak K}$. Moreover, the closability or closedness of $T_n$ 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. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.00312 Zobrazit plný text záznamu View this record from Arxiv