Journal of Convex Analysis 13 (2006), No. 3, 489--497
Copyright Heldermann Verlag 2006
Linear Structures in the Set of Norm-Attaining Functionals on a Banach Space
Stat-Math Division, Indian Statistical Institute, 203 B. T. Road, Kolkata 700 108, India
Equipe d'Analyse, Université Paris VI, 4 Place Jussieu, 75252 Paris, France
We show, among other results, that if the unit ball of the dual of a Banach space X is w*-sequentially compact, the set of norm-attaining functionals contains a separable norm closed subspace M if and only if the dual M* of M is the canonical quotient of X. We provide examples of spaces which cannot be renormed in such a way that the set of norm-attaining functionals become a linear space.
Keywords: Lineability, norm attaining functionals.
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