Full paper in PDF:
$%G. Godefroy and
V. Indumathi, Strong proximinality and polyhedral spaces, Rev. Mat. Complut. 14 (2001), no. 1,
105–125.%$
Equipe d’Analyse Université Paris 6, boite 186 4, Place Jussieu 75252 Paris Cedex 05 — France | Department of Mathematics University of Pondicherry Kalapet Pondicherry 605014 — India |
ABSTRACT
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.
2000 Mathematics Subject Classification: 46B20.