A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866910561759920128 |
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| author | Sain, Debmalya Paul, Kallol Mal, Arpita |
| author_facet | Sain, Debmalya Paul, Kallol Mal, Arpita |
| contents | In this paper, we study Birkhoff-James orthogonality of bounded linear operators and give a complete characterization of Birkhoff-James orthogonality of bounded linear operators on infinite dimensional real normed linear spaces. As an application of the results obtained, we prove a simple but useful characterization of Birkhoff-James orthogonality of bounded linear functionals defined on a real normed linear space, provided the dual space is strictly convex. We also provide separate necessary and sufficient conditions for smoothness of bounded linear operators on infinite dimensional normed linear spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_07713 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space Sain, Debmalya Paul, Kallol Mal, Arpita Functional Analysis 46B20, 47L05 In this paper, we study Birkhoff-James orthogonality of bounded linear operators and give a complete characterization of Birkhoff-James orthogonality of bounded linear operators on infinite dimensional real normed linear spaces. As an application of the results obtained, we prove a simple but useful characterization of Birkhoff-James orthogonality of bounded linear functionals defined on a real normed linear space, provided the dual space is strictly convex. We also provide separate necessary and sufficient conditions for smoothness of bounded linear operators on infinite dimensional normed linear spaces. |
| title | A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space |
| topic | Functional Analysis 46B20, 47L05 |
| url | https://arxiv.org/abs/1706.07713 |