|
Bump functions and differentiability in Banach spaces
Author(s):
D.
J.
Ives
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3583-3588.
MSC (2000):
Primary 46G05;
Secondary 46T20
Posted:
April 24, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that if a Banach space  admits a continuous symmetrically Fréchet subdifferentiable bump function, then  is an Asplund space.
References:
-
- [DGZ]
- R. Deville, G. Godefroy, V. Zizler, Smooth bump functions and geometry of Banach spaces, Mathematika 40, (1993), 305-321. MR 95b:46019
- [EL]
- I. Ekeland, G. Lebourg, Generic Fréchet differentiability and perturbed optimization problems in Banach spaces, Trans. Amer. Math. Soc. 224, (1976), 193-216. MR 55:4254
- [Ha]
- R. Haydon, Trees in renorming theory. Proc. Lond. Math. Soc. 78, (1999), 541-584. MR 2000d:46011
- [LW]
- E. B. Leach, J. H. M. Whitfield, Differentiable functions and rough norms on Banach spaces, Proc. Amer. Math. Soc. 33 (1972), 120-126. MR 45:2471
- [Ph]
- R. R. Phelps, Convex functions, monotone operators, and differentiability, Second edition. Lecture Notes in Mathematics, 1364. Springer-Verlag, Berlin. (1989). MR 90g:46063
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
46G05,
46T20
Retrieve articles in all Journals with MSC
(2000):
46G05,
46T20
Additional Information:
D.
J.
Ives
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
Email:
dean@dps0.math.ucl.ac.uk
DOI:
10.1090/S0002-9939-01-06086-5
PII:
S 0002-9939(01)06086-5
Received by editor(s):
April 14, 2000
Posted:
April 24, 2001
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org