Arkiv för Matematik

  • Ark. Mat.
  • Volume 49, Number 2 (2011), 325-333.

On minimal exposed faces

Francisco Javier García-Pacheco

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Abstract

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.

Note

The author wants to thank the referee for his valuable comments and suggestions.

Article information

Source
Ark. Mat., Volume 49, Number 2 (2011), 325-333.

Dates
Received: 7 September 2009
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907141

Digital Object Identifier
doi:10.1007/s11512-010-0123-3

Mathematical Reviews number (MathSciNet)
MR2826946

Zentralblatt MATH identifier
1267.46019

Rights
2010 © Institut Mittag-Leffler

Citation

García-Pacheco, Francisco Javier. On minimal exposed faces. Ark. Mat. 49 (2011), no. 2, 325--333. doi:10.1007/s11512-010-0123-3. https://projecteuclid.org/euclid.afm/1485907141


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References

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