On minimal exposed faces

Francisco Javier García-Pacheco Department of Mathematics, Texas A&M University

Functional Analysis mathscidoc:1701.12016

Arkiv for Matematik, 49, (2), 325-333, 2009.9
In this paper we consider the problem of the non-empty intersection of exposed faces in a Banach space. We find a sufficient condition to assure that the non-empty intersection of exposed faces is an exposed face. This condition involves the concept of$inner point$. Finally, we also prove that every minimal face of the unit ball must be an extreme point and show that this is not the case at all for minimal exposed faces since we prove that every Banach space with dimension greater than or equal to 2 can be equivalently renormed to have a non-singleton, minimal exposed face.
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  title={On minimal exposed faces},
  author={Francisco Javier García-Pacheco},
  booktitle={Arkiv for Matematik},
Francisco Javier García-Pacheco. On minimal exposed faces. 2009. Vol. 49. In Arkiv for Matematik. pp.325-333. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203630099880000.
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