Strong proximinality and polyhedral spaces.

Gilles Godefroy; V. Indumathi

Revista Matemática Complutense (2001)

  • Volume: 14, Issue: 1, page 105-125
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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Godefroy, Gilles, and Indumathi, V.. "Strong proximinality and polyhedral spaces.." Revista Matemática Complutense 14.1 (2001): 105-125. <http://eudml.org/doc/44461>.

@article{Godefroy2001,
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.},
author = {Godefroy, Gilles, Indumathi, V.},
journal = {Revista Matemática Complutense},
keywords = {Espacios de Banach; Espacio dual; proximinal subspaces; strongly proximinal; polyhedral space; norm-attaining linear functionals; best approximation; continuous selection; almost nearest points; metric projection; annihilator},
language = {eng},
number = {1},
pages = {105-125},
title = {Strong proximinality and polyhedral spaces.},
url = {http://eudml.org/doc/44461},
volume = {14},
year = {2001},
}

TY - JOUR
AU - Godefroy, Gilles
AU - Indumathi, V.
TI - Strong proximinality and polyhedral spaces.
JO - Revista Matemática Complutense
PY - 2001
VL - 14
IS - 1
SP - 105
EP - 125
AB - 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.
LA - eng
KW - Espacios de Banach; Espacio dual; proximinal subspaces; strongly proximinal; polyhedral space; norm-attaining linear functionals; best approximation; continuous selection; almost nearest points; metric projection; annihilator
UR - http://eudml.org/doc/44461
ER -

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