On the numerical index of polyhedral Banach spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866909282937602048 |
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| author | Sain, Debmalya Paul, Kallol Bhunia, Pintu Bag, Santanu |
| author_facet | Sain, Debmalya Paul, Kallol Bhunia, Pintu Bag, Santanu |
| contents | The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any finite-dimensional real polyhedral Banach space, by considering the action of only finitely many functionals, on the unit sphere of the space. We further obtain the exact numerical index of a family of $3$-dimensional polyhedral Banach spaces for the first time, in order to illustrate the applicability of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_04778 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the numerical index of polyhedral Banach spaces Sain, Debmalya Paul, Kallol Bhunia, Pintu Bag, Santanu Functional Analysis Primary 47A12, Secondary 46B20 The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any finite-dimensional real polyhedral Banach space, by considering the action of only finitely many functionals, on the unit sphere of the space. We further obtain the exact numerical index of a family of $3$-dimensional polyhedral Banach spaces for the first time, in order to illustrate the applicability of our method. |
| title | On the numerical index of polyhedral Banach spaces |
| topic | Functional Analysis Primary 47A12, Secondary 46B20 |
| url | https://arxiv.org/abs/1809.04778 |