Some Applications of Simons’ Inequality

@article{Godefroy2000,
abstract = {We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.},
author = {Godefroy, Gilles},
journal = {Serdica Mathematical Journal},
keywords = {Boundaries; Smooth Norms; Norm-attaining Linear Forms; boundaries; smooth norms; norm-attaining linear forms; Simons' inequality; Lebesgue's dominated convergence theorem; Rainwater's theorem; James' characterization of reflexivity; strongly sub-differentiable norm; Asplund space; continuum hypothesis; ZFC},
language = {eng},
number = {1},
pages = {59-78},
publisher = {Institute of Mathematics and Informatics},
title = {Some Applications of Simons’ Inequality},
url = {http://eudml.org/doc/11480},
volume = {26},
year = {2000},
}

TY - JOUR
AU - Godefroy, Gilles
TI - Some Applications of Simons’ Inequality
JO - Serdica Mathematical Journal
PY - 2000
PB - Institute of Mathematics and Informatics
VL - 26
IS - 1
SP - 59
EP - 78
AB - We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.
LA - eng
KW - Boundaries; Smooth Norms; Norm-attaining Linear Forms; boundaries; smooth norms; norm-attaining linear forms; Simons' inequality; Lebesgue's dominated convergence theorem; Rainwater's theorem; James' characterization of reflexivity; strongly sub-differentiable norm; Asplund space; continuum hypothesis; ZFC
UR - http://eudml.org/doc/11480
ER -