Conjugations of Unitary operators, I
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914689647116288 |
|---|---|
| author | Mashreghi, Javad Ptak, Marek Ross, William T. |
| author_facet | Mashreghi, Javad Ptak, Marek Ross, William T. |
| contents | If $U$ is a unitary operator on a separable complex Hilbert space $\mathcal{H}$, an application of the spectral theorem says there is a conjugation $C$ on $\mathcal{H}$ (an antilinear, involutive, isometry on $\mathcal{H}$) for which $
C U C = U^{*}.$ In this paper, we fix a unitary operator $U$ and describe all of the conjugations $C$ which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for $U$ if and only if it is invariant for any conjugation $C$ for which $CUC = U^{*}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conjugations of Unitary operators, I Mashreghi, Javad Ptak, Marek Ross, William T. Functional Analysis 47A465 If $U$ is a unitary operator on a separable complex Hilbert space $\mathcal{H}$, an application of the spectral theorem says there is a conjugation $C$ on $\mathcal{H}$ (an antilinear, involutive, isometry on $\mathcal{H}$) for which $ C U C = U^{*}.$ In this paper, we fix a unitary operator $U$ and describe all of the conjugations $C$ which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for $U$ if and only if it is invariant for any conjugation $C$ for which $CUC = U^{*}$. |
| title | Conjugations of Unitary operators, I |
| topic | Functional Analysis 47A465 |
| url | https://arxiv.org/abs/2402.14995 |