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

  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 separable non-reflexive space, set of norm-attaining functionals, strictly convex norm, Borel class
MSC Classifications: 46B20, 54H05, 46B10 show english descriptions Geometry and structure of normed linear spaces
Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
Duality and reflexivity [See also 46A25]
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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