In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.
@article{urn:eudml:doc:44461,
title = {Strong proximinality and polyhedral spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {14},
year = {2001},
pages = {105-125},
zbl = {0993.46004},
mrnumber = {MR1851725},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44461}
}
Godefroy, Gilles; Indumathi, V. Strong proximinality and polyhedral spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 14 (2001) pp. 105-125. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44461/