Faces and Renormings of ℓ1

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...

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Veröffentlicht in:Mathematics (Basel) 2023-01, Vol.11 (1), p.193
Hauptverfasser: Navarro-Pascual, Juan Carlos, Zarauz-Moreno, Antonio
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
convex set
equivalent renorming of a Banach space
face of a convex set
Mathematics
Norms
Vector space
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Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11010193