When is a CPD weighted shift similar to a subnormal operator?
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929582187216896 |
|---|---|
| author | Jabłoński, Zenon Jan Jung, Il Bong Stochel, Jan |
| author_facet | Jabłoński, Zenon Jan Jung, Il Bong Stochel, Jan |
| contents | We prove that a CPD unilateral weighted shift $W_λ$ of type III is a quasi-affine transform of the operator $M_z$ of multiplication by the independent variable on the $L^2(ρ)$-closure of analytic complex polynomials on the complex plane, where $ρ$ is a measure precisely determined by $W_λ$. By using this model, we provide necessary and sufficient conditions for similarity of $W_λ$ to $M_z$. Necessary conditions for a CPD operator to be similar to a subnormal one are given. A variety of concrete classes of non-subnormal CPD unilateral weighted shifts similar to subnormal operators are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When is a CPD weighted shift similar to a subnormal operator? Jabłoński, Zenon Jan Jung, Il Bong Stochel, Jan Functional Analysis Primary 47B20, 47B37, Secondary 43A35 We prove that a CPD unilateral weighted shift $W_λ$ of type III is a quasi-affine transform of the operator $M_z$ of multiplication by the independent variable on the $L^2(ρ)$-closure of analytic complex polynomials on the complex plane, where $ρ$ is a measure precisely determined by $W_λ$. By using this model, we provide necessary and sufficient conditions for similarity of $W_λ$ to $M_z$. Necessary conditions for a CPD operator to be similar to a subnormal one are given. A variety of concrete classes of non-subnormal CPD unilateral weighted shifts similar to subnormal operators are established. |
| title | When is a CPD weighted shift similar to a subnormal operator? |
| topic | Functional Analysis Primary 47B20, 47B37, Secondary 43A35 |
| url | https://arxiv.org/abs/2411.04911 |