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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reflexivity and sets of Fréchet subdifferentiability


Author: Ondrej Kurka
Journal: Proc. Amer. Math. Soc. 136 (2008), 4467-4473
MSC (2000): Primary 54H05, 46B10, 46G05
Published electronically: June 17, 2008
MathSciNet review: 2431064
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Abstract: We show that the sets of Fréchet subdifferentiability of Lipschitz functions on a Banach space $ X $ are Borel if and only if $ X $ is reflexive. This answers a question of L. Zajíček.


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Additional Information

Ondrej Kurka
Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 00 Prague 8, Czech Republic
Email: ondrej.kurka@mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09425-2
PII: S 0002-9939(08)09425-2
Keywords: Reflexivity, set of Fr\'echet subdifferentiability, Borel set, Suslin set
Received by editor(s): April 5, 2007
Received by editor(s) in revised form: November 1, 2007
Published electronically: June 17, 2008
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.