Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 14, Number 3 (2007), 407-418.
Functionals that do not attain their norm
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.
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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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. doi:10.36045/bbms/1190994202. https://projecteuclid.org/euclid.bbms/1190994202