Subnormal block Toeplitz operators
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910201194479616 |
|---|---|
| author | Abhinand, Mankunikuzhiyil Curto, Raul E. Hwang, In Sung Lee, Woo Young Prasad, Thankarajan |
| author_facet | Abhinand, Mankunikuzhiyil Curto, Raul E. Hwang, In Sung Lee, Woo Young Prasad, Thankarajan |
| contents | In this paper we consider the subnormality of block Toeplitz operators $T_Φ$, where $Φ$ is an $n\times n$ matrix-valued function on the unit circle $\mathbb T$ of the form $$ Φ=QΦ^* \quad \hbox{($Q$ is a finite Blaschke--Potapov product).} $$ This is related to a matrix-valued version of Halmos's Problem 5 and Nakazi-Takahashi Theorem. We ask whether $T_Φ$ is either normal or analytic if $T_Φ$ is subnormal, where $Φ$ is of the above form. We give answers to this problem for different cases of the symbol. Moreover, we provide a sufficient condition for the answer to be affirmative when $Φ^*$ is not of bounded type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subnormal block Toeplitz operators Abhinand, Mankunikuzhiyil Curto, Raul E. Hwang, In Sung Lee, Woo Young Prasad, Thankarajan Functional Analysis 47B20, 47A10 (Primary) In this paper we consider the subnormality of block Toeplitz operators $T_Φ$, where $Φ$ is an $n\times n$ matrix-valued function on the unit circle $\mathbb T$ of the form $$ Φ=QΦ^* \quad \hbox{($Q$ is a finite Blaschke--Potapov product).} $$ This is related to a matrix-valued version of Halmos's Problem 5 and Nakazi-Takahashi Theorem. We ask whether $T_Φ$ is either normal or analytic if $T_Φ$ is subnormal, where $Φ$ is of the above form. We give answers to this problem for different cases of the symbol. Moreover, we provide a sufficient condition for the answer to be affirmative when $Φ^*$ is not of bounded type. |
| title | Subnormal block Toeplitz operators |
| topic | Functional Analysis 47B20, 47A10 (Primary) |
| url | https://arxiv.org/abs/2605.02186 |