Every expansive $ m $-concave operator has $ m $-isometric dilation
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918087848099840 |
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| author | Buchała, Michał |
| author_facet | Buchała, Michał |
| contents | The aim of this paper is to obtain $ m $-isometric dilation of expansive $ m $-concave operator on Hilbert space. The obtained dilation is shown to be minimal. The matrix representation of this dilation is given. It is also proved that in case of 3-concave operators the assumption on expansivity is not necessary. The paper contains an example showing that minimal $ m $-isometric dilations may not be isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Every expansive $ m $-concave operator has $ m $-isometric dilation Buchała, Michał Functional Analysis The aim of this paper is to obtain $ m $-isometric dilation of expansive $ m $-concave operator on Hilbert space. The obtained dilation is shown to be minimal. The matrix representation of this dilation is given. It is also proved that in case of 3-concave operators the assumption on expansivity is not necessary. The paper contains an example showing that minimal $ m $-isometric dilations may not be isomorphic. |
| title | Every expansive $ m $-concave operator has $ m $-isometric dilation |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2507.07252 |