A Gâteaux differentiability space that is not weak Asplund
HTML articles powered by AMS MathViewer
- by Warren B. Moors and Sivajah Somasundaram PDF
- Proc. Amer. Math. Soc. 134 (2006), 2745-2754 Request permission
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
- Mitrofan M. Coban and Petar S. Kenderov, Generic Gateaux differentiability of convex functionals in $C(T)$ and the topological properties of $T$, Mathematics and mathematical education (Bulgarian) (Sunny Beach (SlЪnchev Bryag), 1986) Publ. House Bulgar. Acad. Sci., Sofia, 1986, pp. 141–149. MR 872913
- Marián J. Fabian, Gâteaux differentiability of convex functions and topology, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1997. Weak Asplund spaces; A Wiley-Interscience Publication. MR 1461271
- John R. Giles, Convex analysis with application in the differentiation of convex functions, Research Notes in Mathematics, vol. 58, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. MR 650456
- O. F. K. Kalenda, Weak Stegall spaces, unpublished manuscript, Spring 1997 (3 pages).
- Ondřej Kalenda, Stegall compact spaces which are not fragmentable, Topology Appl. 96 (1999), no. 2, 121–132. MR 1702306, DOI 10.1016/S0166-8641(98)00045-5
- Petar S. Kenderov, Warren B. Moors, and Scott Sciffer, A weak Asplund space whose dual is not weak* fragmentable, Proc. Amer. Math. Soc. 129 (2001), no. 12, 3741–3747. MR 1860511, DOI 10.1090/S0002-9939-01-06002-6
- D. G. Larman and R. R. Phelps, Gâteaux differentiability of convex functions on Banach spaces, J. London Math. Soc. (2) 20 (1979), no. 1, 115–127. MR 545208, DOI 10.1112/jlms/s2-20.1.115
- Warren B. Moors, Some more recent results concerning weak Asplund spaces, Abstr. Appl. Anal. 3 (2005), 307–318. MR 2197122, DOI 10.1155/AAA.2005.307
- Warren B. Moors and Sivajah Somasundaram, Some recent results concerning weak Asplund spaces, Acta Univ. Carolin. Math. Phys. 43 (2002), no. 2, 67–86. 30th Winter School on Abstract Analysis (Lhota nade Rohanovem/Litice u České Lípy, 2002). MR 1979559
- Robert R. Phelps, Convex functions, monotone operators and differentiability, 2nd ed., Lecture Notes in Mathematics, vol. 1364, Springer-Verlag, Berlin, 1993. MR 1238715
- Charles Stegall, A class of topological spaces and differentiation of functions on Banach spaces, Proceedings of the conferences on vector measures and integral representations of operators, and on functional analysis/Banach space geometry (Essen, 1982) Vorlesungen Fachbereich Math. Univ. Essen, vol. 10, Univ. Essen, Essen, 1983, pp. 63–77. MR 730947
- Charles Stegall, The topology of certain spaces of measures, Topology Appl. 41 (1991), no. 1-2, 73–112. MR 1129700, DOI 10.1016/0166-8641(91)90102-R
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
- Received by editor(s): August 31, 2002
- Published electronically: April 7, 2006
- Communicated by: Jonathan M. Borwein
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2745-2754
- MSC (2000): Primary 54C60, 46B20, 54C10
- DOI: https://doi.org/10.1090/S0002-9939-06-08402-4
- MathSciNet review: 2213755