Composition operators on some semi-Hilbert spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912525101039616 |
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| author | Estaremi, Y. Ghafri, M. S. Al |
| author_facet | Estaremi, Y. Ghafri, M. S. Al |
| contents | This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(μ) \). Within the framework of \( A \)-adjoint operators, we characterize conditions under which a composition operator \( C_φ\) is \( A \)-selfadjoint, \( A \)-normal, \( A \)-quasinormal, or \( A \)-unitary, where \( A = M_u \) denotes a positive multiplication operator. Additionally, we provide necessary and sufficient conditions for \( C_φ\) to be an \( A \)-isometry or an \( A \)-partial isometry. Analogous results are also obtained when \( A \) is a positive composition operator. Several examples are presented to illustrate the applicability of the main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Composition operators on some semi-Hilbert spaces Estaremi, Y. Ghafri, M. S. Al Functional Analysis This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(μ) \). Within the framework of \( A \)-adjoint operators, we characterize conditions under which a composition operator \( C_φ\) is \( A \)-selfadjoint, \( A \)-normal, \( A \)-quasinormal, or \( A \)-unitary, where \( A = M_u \) denotes a positive multiplication operator. Additionally, we provide necessary and sufficient conditions for \( C_φ\) to be an \( A \)-isometry or an \( A \)-partial isometry. Analogous results are also obtained when \( A \) is a positive composition operator. Several examples are presented to illustrate the applicability of the main results. |
| title | Composition operators on some semi-Hilbert spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2508.05042 |