Geodesic
Some Applications of Simons’ Inequality
Serdica Mathematical Journal, Tome 26 (2000) no. 1, pp. 59-78.

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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.
Keywords: Boundaries, Smooth Norms, Norm-attaining Linear Forms 
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Godefroy, Gilles. Some Applications of Simons’ Inequality. Serdica Mathematical Journal, Tome 26 (2000) no. 1, pp. 59-78. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_1_a5/