The SOT-closure of the set of 2-isometries
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915481463554048 |
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| author | Scherer, Marcel |
| author_facet | Scherer, Marcel |
| contents | We show that the set of $2$-isometries on an infinite-dimensional Hilbert space is not closed in the strong operator topology. In fact, we prove that its SOT-closure coincides with the set of all expansive operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The SOT-closure of the set of 2-isometries Scherer, Marcel Functional Analysis 47A05 (Primary), 47A20 (Secondary) We show that the set of $2$-isometries on an infinite-dimensional Hilbert space is not closed in the strong operator topology. In fact, we prove that its SOT-closure coincides with the set of all expansive operators. |
| title | The SOT-closure of the set of 2-isometries |
| topic | Functional Analysis 47A05 (Primary), 47A20 (Secondary) |
| url | https://arxiv.org/abs/2509.05083 |