On sup- and inf-attaining functionals
Reflexivity is characterized by the weak-compactness of the unit ball. The weak-compactness of bounded, closed, and convex sets is characterized through sup-attaining functionals in view of the famous James’ theorem. The aim of this mathematical note is to provide the construction of bounded, closed...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2024-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2024-0090 |
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| Summary: | Reflexivity is characterized by the weak-compactness of the unit ball. The weak-compactness of bounded, closed, and convex sets is characterized through sup-attaining functionals in view of the famous James’ theorem. The aim of this mathematical note is to provide the construction of bounded, closed, and convex subsets for which there exists a functional attaining its supremum on such a set but not its infimum. This construction leads to a characterization of reflexivity in the category of normed spaces and a characterization of full norm-attainment also in the category of normed spaces. |
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| ISSN: | 2391-5455 |