Generalized numerical radius inequalities for certain operator matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913645922877440 |
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| author | Sahoo, Satyajit Behera, Narayan |
| author_facet | Sahoo, Satyajit Behera, Narayan |
| contents | In this article, a series of new inequalities involving the $q$-numerical radius for $n\times n$ tridiagonal, and anti-tridiagonal operator matrices has been established. These inequalities serve to establish both lower and upper bounds for the $q$-numerical radius of operator matrices. Additionally, we developed $q$-numerical radius inequalities for $n\times n$ circulant, skew circulant, imaginary circulant, imaginary skew circulant operator matrices. Important examples have been used to illustrate the developed inequalities. In this regard, analytical expressions and a numerical algorithm have also been employed to obtain the $q$-numerical radii. We also provide a concluding section, which may lead to several new problems in this area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized numerical radius inequalities for certain operator matrices Sahoo, Satyajit Behera, Narayan Functional Analysis 47A12, 47A30, 47A63, 15A60 In this article, a series of new inequalities involving the $q$-numerical radius for $n\times n$ tridiagonal, and anti-tridiagonal operator matrices has been established. These inequalities serve to establish both lower and upper bounds for the $q$-numerical radius of operator matrices. Additionally, we developed $q$-numerical radius inequalities for $n\times n$ circulant, skew circulant, imaginary circulant, imaginary skew circulant operator matrices. Important examples have been used to illustrate the developed inequalities. In this regard, analytical expressions and a numerical algorithm have also been employed to obtain the $q$-numerical radii. We also provide a concluding section, which may lead to several new problems in this area. |
| title | Generalized numerical radius inequalities for certain operator matrices |
| topic | Functional Analysis 47A12, 47A30, 47A63, 15A60 |
| url | https://arxiv.org/abs/2501.06995 |