On the numerical radius parallelism and the numerical radius Birkhoff orthogonality
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929610700095488 |
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| author | Bi, Jiaye Xie, Huayou Li, Yongjin |
| author_facet | Bi, Jiaye Xie, Huayou Li, Yongjin |
| contents | In this paper, we generalize the notions of numerical radius parallelism and numerical radius Birkhoff orthogonality, originally formulated for operators on Hilbert spaces, to operators on normed spaces. We then proceed to demonstrate their fundamental properties. Notably, our findings reveal that numerical radius parallelism lacks transitivity, and numerical radius Birkhoff orthogonality is neither left nor right additive. Additionally, we offer characterizations for both concepts. Furthermore, we establish a connection between numerical radius parallelism and numerical radius Birkhoff orthogonality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the numerical radius parallelism and the numerical radius Birkhoff orthogonality Bi, Jiaye Xie, Huayou Li, Yongjin Functional Analysis In this paper, we generalize the notions of numerical radius parallelism and numerical radius Birkhoff orthogonality, originally formulated for operators on Hilbert spaces, to operators on normed spaces. We then proceed to demonstrate their fundamental properties. Notably, our findings reveal that numerical radius parallelism lacks transitivity, and numerical radius Birkhoff orthogonality is neither left nor right additive. Additionally, we offer characterizations for both concepts. Furthermore, we establish a connection between numerical radius parallelism and numerical radius Birkhoff orthogonality. |
| title | On the numerical radius parallelism and the numerical radius Birkhoff orthogonality |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2412.01735 |