Faces and renormings of ℓ1
The faces of the unit ball of a finite-dimensional Banach space are automatically closed. The situation is different in the infinite-dimensional case. In fact, under this last condition, the closure of a face may not be a face. In this paper, we discuss these issues in an expository style. In order...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
MDPI
2023
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/14184 |
| Summary: | The faces of the unit ball of a finite-dimensional Banach space are automatically closed. The situation is different in the infinite-dimensional case. In fact, under this last condition, the closure of a face may not be a face. In this paper, we discuss these issues in an expository style. In order to illustrate the described situation we consider an equivalent renorming of the Banach space ℓ1. |
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