On an open problem regarding totally Fenchel unstable functions
HTML articles powered by AMS MathViewer
- by Radu Ioan Boţ and Ernö Robert Csetnek
- Proc. Amer. Math. Soc. 137 (2009), 1801-1805
- DOI: https://doi.org/10.1090/S0002-9939-08-09738-4
- Published electronically: November 19, 2008
- PDF | Request permission
Abstract:
We give an answer to Problem 11.5 posed in Stephen Simons’s book From Hahn-Banach to Monotonicity.References
- Radu Ioan Boţ and Gert Wanka, A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces, Nonlinear Anal. 64 (2006), no. 12, 2787–2804. MR 2218547, DOI 10.1016/j.na.2005.09.017
- J. Bourgain, A geometric characterization of the Radon-Nikodým property in Banach spaces, Compositio Math. 36 (1978), no. 1, 3–6. MR 515034
- S. Dutta and T. S. S. R. K. Rao, On weak$^*$-extreme points in Banach spaces, J. Convex Anal. 10 (2003), no. 2, 531–539. MR 2044435
- B. V. Godun, Bor-Luh Lin, and S. L. Troyanski, On the strongly extreme points of convex bodies in separable Banach spaces, Proc. Amer. Math. Soc. 114 (1992), no. 3, 673–675. MR 1070518, DOI 10.1090/S0002-9939-1992-1070518-5
- R. E. Huff and P. D. Morris, Dual spaces with the Krein-Milman property have the Radon-Nikodým property, Proc. Amer. Math. Soc. 49 (1975), 104–108. MR 361775, DOI 10.1090/S0002-9939-1975-0361775-9
- Ken Kunen and Haskell Rosenthal, Martingale proofs of some geometrical results in Banach space theory, Pacific J. Math. 100 (1982), no. 1, 153–175. MR 661446, DOI 10.2140/pjm.1982.100.153
- Peter Morris, Disappearance of extreme points, Proc. Amer. Math. Soc. 88 (1983), no. 2, 244–246. MR 695251, DOI 10.1090/S0002-9939-1983-0695251-5
- R. R. Phelps, Extreme points of polar convex sets, Proc. Amer. Math. Soc. 12 (1961), 291–296. MR 121634, DOI 10.1090/S0002-9939-1961-0121634-3
- Stephen Simons, Minimax and monotonicity, Lecture Notes in Mathematics, vol. 1693, Springer-Verlag, Berlin, 1998. MR 1723737, DOI 10.1007/BFb0093633
- Stephen Simons, From Hahn-Banach to monotonicity, 2nd ed., Lecture Notes in Mathematics, vol. 1693, Springer, New York, 2008. MR 2386931
- C. Zălinescu, Convex analysis in general vector spaces, World Scientific Publishing Co., Inc., River Edge, NJ, 2002. MR 1921556, DOI 10.1142/9789812777096
Bibliographic Information
- Radu Ioan Boţ
- Affiliation: Faculty of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
- Email: radu.bot@mathematik.tu-chemnitz.de
- Ernö Robert Csetnek
- Affiliation: Faculty of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
- Email: robert.csetnek@mathematik.tu-chemnitz.de
- Received by editor(s): December 18, 2007
- Received by editor(s) in revised form: July 21, 2008
- Published electronically: November 19, 2008
- Additional Notes: The first author was partially supported by DFG (German Research Foundation), project WA 922/1.
The second author was supported by a Graduate Fellowship of the Free State Saxony, Germany. - Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1801-1805
- MSC (2000): Primary 90C25, 90C46; Secondary 42A50, 90C47, 46B20
- DOI: https://doi.org/10.1090/S0002-9939-08-09738-4
- MathSciNet review: 2470840