Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T09:50:54.386Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 November 2018

Ondřej Kurka
Ondřej Kurka*
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republice-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

46B2054H0546B10separable non-reflexive spaceset of norm-attaining functionalsstrictly convex normBorel class
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 2 , 01 June 2011 , pp. 302 - 310
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Debs, G., Godefroy, G. and Raymond, J. Saint, Topological properties of the set of norm-attaining linear functionals. Canad. J. Math. 47(1995), 318–329.Google Scholar
[2] Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics 64, John Wiley & Sons, New York, 1993.Google Scholar
[3] Kaufman, R., Topics on analytic sets. Fund. Math. 139(1991), 215–229.Google Scholar
[4] Kaufman, R., On smooth norms and analytic sets. Israel J. Math. 116(2000), 21–27. doi:10.1007/BF02773210Google Scholar
[5] Kechris, A. S., Classical descriptive set theory. Graduate Texts in Math. 156, Springer-Verlag, New York, 1995.Google Scholar