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Structure of the Set of Norm-attaining Functionals on Strictly Convex Spaces |
Canad. Math. Bull. 54(2011), 302-310
Published:2011-01-26
Printed: Jun 2011
Printed: Jun 2011
- Ondřej Kurka,
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] |