Journal of Convex Analysis 22 (2015), No. 1, 247--258
Copyright Heldermann Verlag 2015
On Extreme Operators Whose Adjoints Preserve Extreme Points
Ana M. Cabrera-Serrano,
Dep. de Análisis Matemático, Universidad de Granada, Avenida Fuentenueva S/N., 18071 Granada, Spain
anich7@correo.ugr.es
Juan F. Mena-Jurado
Dep. de Análisis Matemático, Universidad de Granada, Avenida Fuentenueva S/N., 18071 Granada, Spain
jfmena@ugr.es
We study Banach spaces X, which we call nice, such that any extreme operator T from a Banach space Y to X is a nice operator, that is, T*, the adjoint of T, preserves extreme points. We get several necessary conditions for being nice. The main result in the paper is the characterization of nice finite-dimensional Banach spaces.
Keywords: Banach space, extreme operator, nice operator.
MSC: 46B20, 46B04
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