Sequences of operators, monotone in the sense of contractive domination
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913181675290624 |
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| author | Hassi, Seppo de Snoo, Henk |
| author_facet | Hassi, Seppo de Snoo, Henk |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00312 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sequences of operators, monotone in the sense of contractive domination Hassi, Seppo de Snoo, Henk Functional Analysis Primary 47A30, 47A63, 47B02, Secondary 47B25, 47B65 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. |
| title | Sequences of operators, monotone in the sense of contractive domination |
| topic | Functional Analysis Primary 47A30, 47A63, 47B02, Secondary 47B25, 47B65 |
| url | https://arxiv.org/abs/2401.00312 |