Functionals that do not attain their norm
Acosta, María D. ; Aizpuru, Antonio ; Aron, Richard M. ; García-Pacheco, Francisco J.
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 407-418 / Harvested from Project Euclid
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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.
Publié le : 2007-09-14
Classification:  norm-attaining functional,  non-norm-attaining functional,  non-density,  density,  46B20,  46B03,  46B07 
@article{1190994202,
     author = {Acosta, Mar\'\i a D. and Aizpuru, Antonio and Aron, Richard M. and Garc\'\i a-Pacheco, Francisco J.},
     title = {Functionals that do not attain their norm},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 407-418},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1190994202}
}

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, Tome 13 (2007) no. 5, pp.  407-418. http://gdmltest.u-ga.fr/item/1190994202/