Abstract

We show, among other results, that if the unit ball of the dual of a Banach space X is w∗w^*-sequentially compact, the set of norm-attaining functionals contains a separable norm closed subspace M if and only if the dual M∗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.

Author information

Contact details are reproduced from the original publication and may be historical.

Pradipta Bandyopadhyay

Stat-Math Division, Indian Statistical Institute, 203 B. T. Road, Kolkata 700 108, India

pradipta@isical.ac.in

Keywords

  • Lineability
  • norm attaining functionals

Mathematics Subject Classification

46B20

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Suggested citation

P. Bandyopadhyay, G. Godefroy. “Linear Structures in the Set of Norm-Attaining Functionals on a Banach Space.” Journal of Convex Analysis 13 (2006), No. 3/4, 489–497. https://doi.org/10.68381/jca13042

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.