$A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866909282957524992 |
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| author | Bhunia, Pintu Feki, Kais Paul, Kallol |
| author_facet | Bhunia, Pintu Feki, Kais Paul, Kallol |
| contents | In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on $\mathcal{H}$. Moreover, a characterization of the $A$-numerical radius parallelism for $A$-rank one operators is proved. As applications of the obtained results, we obtain some $\mathbb{A}$-numerical radius inequalities of operator matrices where $\mathbb{A}$ is the operator diagonal matrix with diagonal entries are positive operator $A$. Some other related results are also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_04522 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications Bhunia, Pintu Feki, Kais Paul, Kallol Functional Analysis 47B65, 47A12, 46C05, 47A05 In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on $\mathcal{H}$. Moreover, a characterization of the $A$-numerical radius parallelism for $A$-rank one operators is proved. As applications of the obtained results, we obtain some $\mathbb{A}$-numerical radius inequalities of operator matrices where $\mathbb{A}$ is the operator diagonal matrix with diagonal entries are positive operator $A$. Some other related results are also investigated. |
| title | $A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications |
| topic | Functional Analysis 47B65, 47A12, 46C05, 47A05 |
| url | https://arxiv.org/abs/2001.04522 |