Bulletin of the Belgian Mathematical Society - Simon Stevin

Functionals that do not attain their norm

María D. Acosta, Antonio Aizpuru, Richard M. Aron, and Francisco J. García-Pacheco

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We study the set of non-norm-attaining functionals on a Banach space, giving a sufficient condition for the density of this set. We also find a large class of Banach spaces for which the set of norm-attaining functionals is (dense-) lineable. In addition, among other results, we provide a new proof of the fact that every real Banach space can be equivalently renormed so that the set of non-norm-attaining functionals is non-dense.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 3 (2007), 407-418.

First available in Project Euclid: 28 September 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces 46B03: Isomorphic theory (including renorming) of Banach spaces 46B07: Local theory of Banach spaces

norm-attaining functional non-norm-attaining functional non-density density


Acosta, María D.; Aizpuru, Antonio; Aron, Richard M.; García-Pacheco, Francisco J. Functionals that do not attain their norm. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 407--418. https://projecteuclid.org/euclid.bbms/1190994202

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