On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866910563824566272 |
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| author | Bhunia, Pintu Sain, Debmalya Paul, Kallol |
| author_facet | Bhunia, Pintu Sain, Debmalya Paul, Kallol |
| contents | We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space $\mathcal{X}$. We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on $\mathcal{L}(\mathcal{X})$ which is equivalent to the usual operator norm on $\mathcal{L}(\mathcal{X})$. We introduce the Davis-Wielandt index of a normed linear space and compute its value explicitly in case of some particular polyhedral Banach spaces. We also present a general method to estimate the Davis-Wielandt index of any polyhedral Banach space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_15323 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space Bhunia, Pintu Sain, Debmalya Paul, Kallol Functional Analysis Primary 47A12, Secondary 46B20, 47L05 We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space $\mathcal{X}$. We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on $\mathcal{L}(\mathcal{X})$ which is equivalent to the usual operator norm on $\mathcal{L}(\mathcal{X})$. We introduce the Davis-Wielandt index of a normed linear space and compute its value explicitly in case of some particular polyhedral Banach spaces. We also present a general method to estimate the Davis-Wielandt index of any polyhedral Banach space. |
| title | On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space |
| topic | Functional Analysis Primary 47A12, Secondary 46B20, 47L05 |
| url | https://arxiv.org/abs/2006.15323 |