On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914517186772992 |
|---|---|
| author | Loaiza, Maribel Morales-Ramos, Miguel Antonio Ramírez-Mora, María del Rosario Ramírez-Ortega, Josué |
| author_facet | Loaiza, Maribel Morales-Ramos, Miguel Antonio Ramírez-Mora, María del Rosario Ramírez-Ortega, Josué |
| contents | In the context of studying $C^*$-algebras generated by Toeplitz operators acting on the poly-Bergman space $\mathcal{A}^2_{n}(Π)$ of the upper half-plane $Π$, we introduce a system of all-but-one orthogonal projections in generic position. We show that the $C^*$-algebra generated by these orthoprojections is closely related to the $C^*$-algebra generated by all Toeplitz operators with vertical symbols satisfying boundary conditions. This result suggests a new approach in the study of Toeplitz operators acting on other reproducing kernel Hilbert spaces. Furthermore, the range of one of the orthoprojections herein has a reproducing kernel expressed in terms of the digamma and the Nielsen's beta functions. The harmonic function also emerges in this development. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26918 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols Loaiza, Maribel Morales-Ramos, Miguel Antonio Ramírez-Mora, María del Rosario Ramírez-Ortega, Josué Operator Algebras In the context of studying $C^*$-algebras generated by Toeplitz operators acting on the poly-Bergman space $\mathcal{A}^2_{n}(Π)$ of the upper half-plane $Π$, we introduce a system of all-but-one orthogonal projections in generic position. We show that the $C^*$-algebra generated by these orthoprojections is closely related to the $C^*$-algebra generated by all Toeplitz operators with vertical symbols satisfying boundary conditions. This result suggests a new approach in the study of Toeplitz operators acting on other reproducing kernel Hilbert spaces. Furthermore, the range of one of the orthoprojections herein has a reproducing kernel expressed in terms of the digamma and the Nielsen's beta functions. The harmonic function also emerges in this development. |
| title | On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2604.26918 |