Approximate Birkhoff-James orthogonality in the space of bounded linear operators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866929454378385408 |
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| author | Paul, Kallol Sain, Debmalya Mal, Arpita |
| author_facet | Paul, Kallol Sain, Debmalya Mal, Arpita |
| contents | There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete characterization of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on Hilbert space of any dimension is obtained which improves on the recent result by Chmieliński et al. [ J. Chmieliński, T. Stypula and P. Wójcik, \textit{Approximate orthogonality in normed spaces and its applications}, Linear Algebra and its Applications, \textbf{531} (2017), 305--317.], in which they characterized approximate Birkhoff-James orthogonality of linear operators on finite dimensional Hilbert space and also of compact operators on any Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_09237 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Approximate Birkhoff-James orthogonality in the space of bounded linear operators Paul, Kallol Sain, Debmalya Mal, Arpita Functional Analysis 46B28, 47L05, 47L25 There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete characterization of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on Hilbert space of any dimension is obtained which improves on the recent result by Chmieliński et al. [ J. Chmieliński, T. Stypula and P. Wójcik, \textit{Approximate orthogonality in normed spaces and its applications}, Linear Algebra and its Applications, \textbf{531} (2017), 305--317.], in which they characterized approximate Birkhoff-James orthogonality of linear operators on finite dimensional Hilbert space and also of compact operators on any Hilbert space. |
| title | Approximate Birkhoff-James orthogonality in the space of bounded linear operators |
| topic | Functional Analysis 46B28, 47L05, 47L25 |
| url | https://arxiv.org/abs/1706.09237 |