On similarity to contraction semigroups and tensor products, I
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918134826401792 |
|---|---|
| author | Oliva-Maza, J. Tomilov, Y. |
| author_facet | Oliva-Maza, J. Tomilov, Y. |
| contents | In the context of finite tensor products of Hilbert spaces, we prove that similarity of a tensor product of operator semigroups to a contraction semigroup is equivalent to the corresponding similarity for each factor, after an appropriate rescaling. A similar result holds with contractivity replaced by quasi-contractivity. This splitting phenomenon allows us to construct new and, in a sense, the strongest possible examples of $C_0$-semigroups not similar to contractions, thus completing an important chapter of the theory. We also address the discrete setting and relate it to our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On similarity to contraction semigroups and tensor products, I Oliva-Maza, J. Tomilov, Y. Functional Analysis 47D03, 47A65, 47A20, 47A80 In the context of finite tensor products of Hilbert spaces, we prove that similarity of a tensor product of operator semigroups to a contraction semigroup is equivalent to the corresponding similarity for each factor, after an appropriate rescaling. A similar result holds with contractivity replaced by quasi-contractivity. This splitting phenomenon allows us to construct new and, in a sense, the strongest possible examples of $C_0$-semigroups not similar to contractions, thus completing an important chapter of the theory. We also address the discrete setting and relate it to our results. |
| title | On similarity to contraction semigroups and tensor products, I |
| topic | Functional Analysis 47D03, 47A65, 47A20, 47A80 |
| url | https://arxiv.org/abs/2509.01005 |