# Strong proximinality and polyhedral spaces.

Revista Matemática Complutense (2001)

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

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topGodefroy, 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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