Transitivity of proximinality and norm attaining functionals

Darapaneni Narayana, and T. S. S. R. K. Rao. "Transitivity of proximinality and norm attaining functionals." Colloquium Mathematicae 104.1 (2006): 1-19. <http://eudml.org/doc/283885>.

@article{DarapaneniNarayana2006,
abstract = {We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in $\widetilde\{R(1)\}$ spaces and generally by taking quotients by proximinal subspaces. We show, for (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and show that, for some particular hyperplanes of c₀, linearity and orthogonal linearity coincide for the set of norm attaining functionals.},
author = {Darapaneni Narayana, T. S. S. R. K. Rao},
journal = {Colloquium Mathematicae},
keywords = {; norm attaining functional; orthogonal linearity;  space;  space; transitivity of proximinality},
language = {eng},
number = {1},
pages = {1-19},
title = {Transitivity of proximinality and norm attaining functionals},
url = {http://eudml.org/doc/283885},
volume = {104},
year = {2006},
}

TY - JOUR
AU - Darapaneni Narayana
AU - T. S. S. R. K. Rao
TI - Transitivity of proximinality and norm attaining functionals
JO - Colloquium Mathematicae
PY - 2006
VL - 104
IS - 1
SP - 1
EP - 19
AB - We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in $\widetilde{R(1)}$ spaces and generally by taking quotients by proximinal subspaces. We show, for (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and show that, for some particular hyperplanes of c₀, linearity and orthogonal linearity coincide for the set of norm attaining functionals.
LA - eng
KW - ; norm attaining functional; orthogonal linearity;  space;  space; transitivity of proximinality
UR - http://eudml.org/doc/283885
ER -