Preservation of Extreme Points

Juan Francisco Mena-Jurado and Juan Carlos Navarro-Pascual
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Juan Francisco Mena-Jurado: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Juan Carlos Navarro-Pascual: Departamento de Matemáticas, Facultad de Ciencias Experimentales, Universidad de Almería, 04120 Almería, Spain

Mathematics, 2022, vol. 10, issue 13, 1-5

Abstract: We characterize the extreme points of the closed unit ball of the dual of a Banach space which are preserved by the adjoint of any extreme operator. The result is related to the structure topology introduced by Alfsen and Effros on the set of all extreme points in the dual of any Banach space. As a consequence, we prove that c 0 ( I ) is the only Banach space such that the adjoint of every extreme operator taking values into it preserves extreme points.

Keywords: Banach space; extreme operator; structure topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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