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# Structure of the Set of Norm-attaining Functionals on Strictly Convex Spaces

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Published:2011-01-26
Printed: Jun 2011
• Ondřej Kurka,
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
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## Abstract

Let $X$ be a separable non-reflexive Banach space. We show that there is no Borel class which contains the set of norm-attaining functionals for every strictly convex renorming of $X$.
 Keywords: separable non-reflexive space, set of norm-attaining functionals, strictly convex norm, Borel class
 MSC Classifications: 46B20 - Geometry and structure of normed linear spaces 54H05 - Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 46B10 - Duality and reflexivity [See also 46A25]

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