Characterizations of $w_ρ$-Birkhoff--James orthogonality and $w_ρ$-parallelism
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911875406495744 |
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| author | Kittaneh, Fuad Zamani, Ali |
| author_facet | Kittaneh, Fuad Zamani, Ali |
| contents | We study the concepts of Birkhoff--James orthogonality and parallelism in Hilbert space operators, induced by the operator radius norm $w_ρ(\cdot)$. In particular, we completely characterize Birkhoff--James orthogonality and parallelism with respect to $w_ρ(\cdot)$. As an application of the results presented, we obtain a well-known characterization due to R.~Bhatia and P.~Šemrl for the classical Birkhoff--James orthogonality of Hilbert space operators. Some other related results are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizations of $w_ρ$-Birkhoff--James orthogonality and $w_ρ$-parallelism Kittaneh, Fuad Zamani, Ali Functional Analysis 46B20, 47A12, 47A20, 47A30, 47L05 We study the concepts of Birkhoff--James orthogonality and parallelism in Hilbert space operators, induced by the operator radius norm $w_ρ(\cdot)$. In particular, we completely characterize Birkhoff--James orthogonality and parallelism with respect to $w_ρ(\cdot)$. As an application of the results presented, we obtain a well-known characterization due to R.~Bhatia and P.~Šemrl for the classical Birkhoff--James orthogonality of Hilbert space operators. Some other related results are also discussed. |
| title | Characterizations of $w_ρ$-Birkhoff--James orthogonality and $w_ρ$-parallelism |
| topic | Functional Analysis 46B20, 47A12, 47A20, 47A30, 47L05 |
| url | https://arxiv.org/abs/2405.07629 |