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Operator Algebras, Operator Theory and Applications pp 167–172Cite as

Nowhere Density of the Set of Non-norm-attaining Functionals

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 195))

Abstract

In this short note we prove that every real Banach space with separable dual can be equivalently renormed so that the set of non-norm-attaining functionals on it is nowhere dense. This solves a question proposed by Enflo.

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References

  1. A. Aizpuru, M.D. Acosta, R.M. Aron, and F.J. García-Pacheco, Functionals that do not attain their norm. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 407–418.

    MATH  MathSciNet  Google Scholar 

  2. M.D. Acosta and M.R. Galán, New characterizations of the reflexivity in terms of the set of norm-attaining functionals. Canad. Math. Bull. 41 (1998), 279–289.

    MATH  MathSciNet  Google Scholar 

  3. R. Deville, G. Godefroy and V. Zizler, Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics 64, New York, 1993.

    Google Scholar 

  4. J. Diestel, Geometry of Banach spaces-selected topics. Lecture Notes in Mathematics 485, Springer-Verlag, Berlin-New York, 1975.

    MATH  Google Scholar 

  5. F.J. García-Pacheco and A. Miralles, Real renormings on complex Banach spaces. Chin. Ann. Math. Ser. B 29 (2008), 239–246.

    Article  MATH  MathSciNet  Google Scholar 

  6. F. J. García-Pacheco, The minimum-norm problem for translations. Preprint.

    Google Scholar 

  7. M. Jiménez-Sevilla and J.P. Moreno, A note on norm-attaining functionals. Proc. Amer. Math. Soc. 126 (1998), 1989–1997.

    Article  MathSciNet  Google Scholar 

  8. W. Johnson and J. Lindenstrauss, Handbook of the geometry of Banach spaces II North-Holland, Amsterdam, 2003.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX, 77843, USA

    Francisco J. García-Pacheco

Authors
  1. Francisco J. García-Pacheco
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Editor information

Editors and Affiliations

  1. School for Computer, Statistical and Mathematical Sciences, North-West University, 2520, Potchefstroom, South Africa

    J. J. Grobler

  2. Department of Mathematical Sciences, University of South Africa, PO Box 392, 0003 UNISA, South Africa

    L. E. Labuschagne

  3. John Knopfmacher Centre for Applicable Analysis and Number Theory School of Mathematics, University of the Witwatersrand, 2050 WITS, South Africa

    M. Möller

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© 2009 Birkhäuser Verlag Basel/Switzerland

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García-Pacheco, F.J. (2009). Nowhere Density of the Set of Non-norm-attaining Functionals. In: Grobler, J.J., Labuschagne, L.E., Möller, M. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 195. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0174-0_7

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