Abstract
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.
Citation
María D. Acosta. Antonio Aizpuru. Richard M. Aron. Francisco J. García-Pacheco. "Functionals that do not attain their norm." Bull. Belg. Math. Soc. Simon Stevin 14 (3) 407 - 418, September 2007. https://doi.org/10.36045/bbms/1190994202
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