On the Crawford number attaining operators
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866908275562250240 |
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| author | Choi, Geunsu Lee, Han Ju |
| author_facet | Choi, Geunsu Lee, Han Ju |
| contents | We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the RNP, then the set of Crawford number attaining operators is dense in the space of bounded linear operators. We also see among others that the set of Crawford number attaining operators may be dense in the space of all bounded linear operators while they do not coincide, by observing the case of compact operators when the Banach space has a 1-unconditional basis. Furthermore, we show a Bishop-Phelps-Bollobás type property for the Crawford number for certain Banach spaces, and we finally discuss some difficulties and possible problems on the topic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_10031 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Crawford number attaining operators Choi, Geunsu Lee, Han Ju Functional Analysis Primary: 46B20, Secondary: 46B04, 46B25, 47A12 We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the RNP, then the set of Crawford number attaining operators is dense in the space of bounded linear operators. We also see among others that the set of Crawford number attaining operators may be dense in the space of all bounded linear operators while they do not coincide, by observing the case of compact operators when the Banach space has a 1-unconditional basis. Furthermore, we show a Bishop-Phelps-Bollobás type property for the Crawford number for certain Banach spaces, and we finally discuss some difficulties and possible problems on the topic. |
| title | On the Crawford number attaining operators |
| topic | Functional Analysis Primary: 46B20, Secondary: 46B04, 46B25, 47A12 |
| url | https://arxiv.org/abs/2201.10031 |