Open AccessStrong proximinality and polyhedral spaces
Author(s) -
Gilles Godefroy,
V. Indumathi
Publication year - 2001
Publication title -
revista matemática complutense
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.093
H-Index - 24
eISSN - 1696-8220
pISSN - 1139-1138
DOI - 10.5209/rev_rema.2001.v14.n1.17047
Subject(s) - mathematics , hyperplane , subspace topology , norm (philosophy) , combinatorics , set (abstract data type) , pure mathematics , mathematical analysis , law , political science , computer science , programming language
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