Isometric and Quasi-isometric weighted composition operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908556385583104 |
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| author | Ghafri, M. S. Al Estaremi, Y. Gashti, M. Z. |
| author_facet | Ghafri, M. S. Al Estaremi, Y. Gashti, M. Z. |
| contents | In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted composition operators on the Hilbert space $L^2(μ)$. Also, we find that normal-$m$-isometry and normal quasi-$m$-isometry weighted composition operators have finite spectrum. Consequently we have the results for composition and multiplication operators. In addition, we prove that for $m\geq 2$, a multiplication operator is $m$-isometry (quasi-$m$-isometry) if and only if it is $2$-isometry (quasi-$2$-isometry). Some examples are provided to illustrate our results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isometric and Quasi-isometric weighted composition operators Ghafri, M. S. Al Estaremi, Y. Gashti, M. Z. Functional Analysis In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted composition operators on the Hilbert space $L^2(μ)$. Also, we find that normal-$m$-isometry and normal quasi-$m$-isometry weighted composition operators have finite spectrum. Consequently we have the results for composition and multiplication operators. In addition, we prove that for $m\geq 2$, a multiplication operator is $m$-isometry (quasi-$m$-isometry) if and only if it is $2$-isometry (quasi-$2$-isometry). Some examples are provided to illustrate our results. |
| title | Isometric and Quasi-isometric weighted composition operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.16969 |