|
A Gâteaux differentiability space that is not weak Asplund
Authors:
Warren B. Moors and Sivajah Somasundaram
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2745-2754
MSC (2000):
Primary 54C60, 46B20, 54C10
Posted:
April 7, 2006
MathSciNet review:
2213755
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this paper we construct a Gâteaux differentiability space that is not a weak Asplund space. Thus we answer a question raised by David Larman and Robert Phelps from 1979.
References
- 1.
M. M. Coban and P. S. Kenderov, Generic Gâteaux differentiability of convex functionals in
 and the topological properties of  , Proceedings of 15th Spring Conference of the Union of Bulgarian Mathematicians, Sljancev Brjag, (1986), 141-149. MR 0872913 (88d:46037)
- 2.
M. J. Fabian, Gâteaux differentiability of convex functions and topology: Weak Asplund spaces, Canadian Mathematical Society Series of Monographs and Advanced Texts. Wiley-Interscience, New York, 1997. MR 1461271 (98h:46009)
- 3.
J. R. Giles, Convex Analysis with Application in Differentiation of Convex Functions, Research Notes in Mathematics, 58 Pitman, Melbourne, 1982. MR 0650456 (83g:46001)
- 4.
O. F. K. Kalenda, Weak Stegall spaces, unpublished manuscript, Spring 1997 (3 pages).
- 5.
O. F. K. Kalenda, Stegall compact spaces which are not fragmentable, Topology Appl. 96 (1999), 121-132. MR 1702306 (2000i:54027)
- 6.
P. S. Kenderov, W. B. Moors and S. Sciffer, A weak Asplund space whose dual is not weak
 fragmentable, Proc. Amer. Math. Soc. 129 (2001), 3741-3747. MR 1860511 (2002h:54014)
- 7.
D. G. Larman and R. R. Phelps, Gâteaux differentiability of convex functions on Banach spaces, J. London Math. Soc. 20 (1979), 115-127. MR 0545208 (80m:46017)
- 8.
W. B. Moors, Some more recent results concerning weak Asplund spaces, Abstr. Appl. Anal. 2005 (2005), 307-318. MR 2197122
- 9.
W. B. Moors and S. Somasundaram, Some recent results concerning weak Asplund spaces, Acta Univ. Carolin. Math. Phys. 43 (2002), 67-86. MR 1979559 (2004e:46027)
- 10.
R. R. Phelps, Convex functions, monotone operators and differentiability, Lecture notes in Mathematics, Springer-Verlag, Berlin, 1993. MR 1238715 (94f:46055)
- 11.
C. Stegall, A class of topological spaces and differentiability, Vorlesungen aus dem Fachbereich Mathematik der Universität Essen 10 (1983), 63-77. MR 0730947 (85j:46026)
- 12.
C. Stegall, The topology of certain spaces of measures, Topology Appl. 41 (1991), 73-112. MR 1129700 (93d:46067)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2000):
54C60,
46B20,
54C10
Retrieve articles in all journals
with MSC (2000):
54C60,
46B20,
54C10
Additional Information
Warren B. Moors
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
Email:
moors@math.auckland.ac.nz
Sivajah Somasundaram
Affiliation:
Department of Mathematics, The University of Waikato, Private Bag 3105, Hamilton 2001, New Zealand
Email:
ss15@math.waikato.ac.nz
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08402-4
PII:
S 0002-9939(06)08402-4
Keywords:
Weak Asplund space,
G\^ateaux differentiability space,
Stegall space
Received by editor(s):
August 31, 2002
Posted:
April 7, 2006
Communicated by:
Jonathan M. Borwein
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
|
