Approximate Birkhoff-James orthogonality and smoothness in the space of bounded linear operators
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866916351521587200 |
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| author | Mal, Arpita Paul, Kallol Rao, T. S. S. R. K. Sain, Debmalya |
| author_facet | Mal, Arpita Paul, Kallol Rao, T. S. S. R. K. Sain, Debmalya |
| contents | We study approximate Birkhoff-James orthogonality of bounded linear operators defined between normed linear spaces $\mathbb{X}$ and $\mathbb{Y}.$ As an application of the results obtained, we characterize smoothness of a bounded linear operator $T$ under the condition that $\mathbb{K}(\mathbb{X},\mathbb{Y}),$ the space of compact linear operators is an $M-$ideal in $\mathbb{L}(\mathbb{X},\mathbb{Y}),$ the space of bounded linear operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1811_02772 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Approximate Birkhoff-James orthogonality and smoothness in the space of bounded linear operators Mal, Arpita Paul, Kallol Rao, T. S. S. R. K. Sain, Debmalya Functional Analysis Primary 46B28, Secondary 47L05, 46B20 We study approximate Birkhoff-James orthogonality of bounded linear operators defined between normed linear spaces $\mathbb{X}$ and $\mathbb{Y}.$ As an application of the results obtained, we characterize smoothness of a bounded linear operator $T$ under the condition that $\mathbb{K}(\mathbb{X},\mathbb{Y}),$ the space of compact linear operators is an $M-$ideal in $\mathbb{L}(\mathbb{X},\mathbb{Y}),$ the space of bounded linear operators. |
| title | Approximate Birkhoff-James orthogonality and smoothness in the space of bounded linear operators |
| topic | Functional Analysis Primary 46B28, Secondary 47L05, 46B20 |
| url | https://arxiv.org/abs/1811.02772 |