Some spectral properties and convergence of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916752634413056 |
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| author | Al, Pembe Ipek Ismailov, Zameddin I. Kittaneh, Fuad Sahoo, Satyajit |
| author_facet | Al, Pembe Ipek Ismailov, Zameddin I. Kittaneh, Fuad Sahoo, Satyajit |
| contents | In this study, some estimates are given for the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number via the $ A$-numerical radius and $ A$-Crawford number for the $ A $-bounded linear operators in any complex semi-Hilbert space, respectively. Then, some evolutions are studied for the tensor product of two operators. Lastly, some convergence properties of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number, via the $ A$-uniform convergence of operator sequences, are investigated. We also considered several examples to illustrate our results. Finally, a few applications of some operator functions classes are also given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some spectral properties and convergence of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number Al, Pembe Ipek Ismailov, Zameddin I. Kittaneh, Fuad Sahoo, Satyajit Functional Analysis 47A05, 47A12, 47A30, 47A63 In this study, some estimates are given for the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number via the $ A$-numerical radius and $ A$-Crawford number for the $ A $-bounded linear operators in any complex semi-Hilbert space, respectively. Then, some evolutions are studied for the tensor product of two operators. Lastly, some convergence properties of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number, via the $ A$-uniform convergence of operator sequences, are investigated. We also considered several examples to illustrate our results. Finally, a few applications of some operator functions classes are also given. |
| title | Some spectral properties and convergence of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number |
| topic | Functional Analysis 47A05, 47A12, 47A30, 47A63 |
| url | https://arxiv.org/abs/2505.16924 |