Abstract

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∗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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Banach space
  • extreme operator
  • nice operator

Mathematics Subject Classification

46B20, 46B04

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Suggested citation

A. M. Cabrera-Serrano, J. F. Mena-Jurado. “On Extreme Operators Whose Adjoints Preserve Extreme Points.” Journal of Convex Analysis 22 (2015), No. 1, 247–258. https://doi.org/10.68381/jca22012

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.