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Reflexivity and sets of Fréchet subdifferentiability
Author(s):
Ondrej
Kurka
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4467-4473.
MSC (2000):
Primary 54H05, 46B10, 46G05
Posted:
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  are Borel if and only if  is reflexive. This answers a question of L. Zajíček.
References:
-
- 1.
- R. C. James: Characterizations of reflexivity, Studia Math., 23 (1964), 205-216. MR 0170192 (30:431)
- 2.
- A. S. Kechris: Classical descriptive set theory, Springer, New York, 1995. MR 1321597 (96e:03057)
- 3.
- O. Kurka: On Borel classes of sets of Fréchet subdifferentiability, Bull. Polish Acad. Sci. Math., 55 (2007), 201-209. MR 2346098
- 4.
- E. McShane: Extension of range of functions, Bull. Amer. Math. Soc., 40 (1934), 837-842. MR 1562984
- 5.
- M. Šmídek: Measureability of some subsets of spaces of functions (in Czech), Charles University, Prague, 1994.
- 6.
- L. Zajíček: Frechet differentiability, strict differentiability and subdifferentiability, Czechoslovak Math. J., 41 (1991), 471-489. MR 1117801 (92j:46081)
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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:
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
Posted:
June 17, 2008
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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