Linear isometries of Hol(D)
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929344967868416 |
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| author | Chalendar, I. Oger, L. Partington, J. R. |
| author_facet | Chalendar, I. Oger, L. Partington, J. R. |
| contents | A complete characterisation is given of all the linear isometries of the Fréchet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of a particular form. Operators similar to an isometry are also classified. Further, the larger class of operators isometric when restricted to one of the defining seminorms is identified. Finally, the spectra of such operators are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear isometries of Hol(D) Chalendar, I. Oger, L. Partington, J. R. Complex Variables 47B33, 30H05, 47A10 A complete characterisation is given of all the linear isometries of the Fréchet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of a particular form. Operators similar to an isometry are also classified. Further, the larger class of operators isometric when restricted to one of the defining seminorms is identified. Finally, the spectra of such operators are studied. |
| title | Linear isometries of Hol(D) |
| topic | Complex Variables 47B33, 30H05, 47A10 |
| url | https://arxiv.org/abs/2402.14671 |