Faces and Renormings of ℓ 1

Juan Carlos Navarro-Pascual () and Antonio Zarauz-Moreno
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Juan Carlos Navarro-Pascual: Departamento de Matemáticas, Facultad de Ciencias Experimentales, Universidad de Almería, 04120 Almería, Spain
Antonio Zarauz-Moreno: Departamento de Matemáticas, Facultad de Ciencias Experimentales, Universidad de Almería, 04120 Almería, Spain

Mathematics, 2022, vol. 11, issue 1, 1-11

Abstract: 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 ℓ 1 .

Keywords: convex set; face of a convex set; equivalent renorming of a Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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