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On the Crawford number attaining operators
- Authors
- Choi, Geunsu; Lee, Han Ju
- Issue Date
- Sep-2023
- Publisher
- Universidad Complutense de Madrid
- Keywords
- Banach space; Norm attainment; Numerical radius; Crawford number
- Citation
- Revista Matemática Complutense, v.36, no.3, pp 841 - 857
- Pages
- 17
- Indexed
- SCIE
SCOPUS
- Journal Title
- Revista Matemática Complutense
- Volume
- 36
- Number
- 3
- Start Page
- 841
- End Page
- 857
- ISSN
- 1139-1138
1988-2807
- Abstract
- We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the Radon-NikodATIN SMALL LETTER Y WITH ACUTEm property, 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 is 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-Bollobas type property for the Crawford number for certain Banach spaces, and we finally discuss some difficulties and possible problems on the topic.
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)