An Exposition on Weak Stability of Operators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916350450991104 |
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| author | Kubrusly, C. S. |
| author_facet | Kubrusly, C. S. |
| contents | This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability, containing a few new results and some unanswered questions. It also gives an updated review of the literature on the weak stability of operators over the past sixty years, including present-day research trends. It is verified that the majority of the weak stability literature is concentrated on Hilbert-space operators. We discuss why this preference occurs and also why the weak stability of unitary operators is central to the Hilbert-space stability problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04186 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Exposition on Weak Stability of Operators Kubrusly, C. S. Functional Analysis 47A15, 47A45, 4BA15, A7B20 This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability, containing a few new results and some unanswered questions. It also gives an updated review of the literature on the weak stability of operators over the past sixty years, including present-day research trends. It is verified that the majority of the weak stability literature is concentrated on Hilbert-space operators. We discuss why this preference occurs and also why the weak stability of unitary operators is central to the Hilbert-space stability problem. |
| title | An Exposition on Weak Stability of Operators |
| topic | Functional Analysis 47A15, 47A45, 4BA15, A7B20 |
| url | https://arxiv.org/abs/2408.04186 |