Full paper in PDF:
$%G. Godefroy and V. Indumathi, Strong proximinality and polyhedral spaces, Rev. Mat. Complut. 14 (2001), no. 1, 105125.%$

Strong Proximinality and Polyhedral Spaces
Equipe d’Analyse
Université Paris 6, boite 186
4, Place Jussieu
75252 Paris Cedex 05 — France
Department of Mathematics
University of Pondicherry
Pondicherry 605014 — India

Received: January 10, 2000
Revised: October 24, 2000


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.