Weighted composition operators on weighted Dirichlet spaces: boundedness, compactness and spectral properties
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914315740643328 |
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| author | Sen, Anirban |
| author_facet | Sen, Anirban |
| contents | We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend earlier work on unweighted composition operators and highlight the close interplay between the operator theoretic behavior of weighted composition operators and the function theoretic properties of their inducing functions. Several examples are provided to illustrate the applicability of the obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted composition operators on weighted Dirichlet spaces: boundedness, compactness and spectral properties Sen, Anirban Functional Analysis 47B38, 47B91, 47B33, 30H05 We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend earlier work on unweighted composition operators and highlight the close interplay between the operator theoretic behavior of weighted composition operators and the function theoretic properties of their inducing functions. Several examples are provided to illustrate the applicability of the obtained results. |
| title | Weighted composition operators on weighted Dirichlet spaces: boundedness, compactness and spectral properties |
| topic | Functional Analysis 47B38, 47B91, 47B33, 30H05 |
| url | https://arxiv.org/abs/2602.08651 |