A functional model and tridiagonalisation for symmetric anti-linear operators
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917743737962496 |
|---|---|
| author | Pushnitski, Alexander Štampach, František |
| author_facet | Pushnitski, Alexander Štampach, František |
| contents | We consider the class of bounded symmetric anti-linear operators $B$ with a cyclic vector. We associate with $B$ the spectral data consisting of a probability measure and a function. In terms of the spectral data of $B$, we introduce a functional model operator $\mathcal{B}$ acting on a model space. We prove an anti-linear variant of the spectral theorem demonstrating that $B$ is unitarily equivalent to $\mathcal{B}$. Next, we show that $B$ is also unitarily equivalent to an anti-linear tridiagonal operator and discuss connection with orthogonal polynomials in the anti-linear setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A functional model and tridiagonalisation for symmetric anti-linear operators Pushnitski, Alexander Štampach, František Spectral Theory Functional Analysis 47B36, 47H99, 47S99 We consider the class of bounded symmetric anti-linear operators $B$ with a cyclic vector. We associate with $B$ the spectral data consisting of a probability measure and a function. In terms of the spectral data of $B$, we introduce a functional model operator $\mathcal{B}$ acting on a model space. We prove an anti-linear variant of the spectral theorem demonstrating that $B$ is unitarily equivalent to $\mathcal{B}$. Next, we show that $B$ is also unitarily equivalent to an anti-linear tridiagonal operator and discuss connection with orthogonal polynomials in the anti-linear setting. |
| title | A functional model and tridiagonalisation for symmetric anti-linear operators |
| topic | Spectral Theory Functional Analysis 47B36, 47H99, 47S99 |
| url | https://arxiv.org/abs/2402.01237 |