Locating subsets of a normed space
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- by Hajime Ishihara and Luminiţa Vîţă PDF
- Proc. Amer. Math. Soc. 131 (2003), 3231-3239 Request permission
Abstract:
Within the framework of Bishop’s constructive mathematics, we give conditions under which a bounded convex subset of a uniformly smooth normed space over ${\mathbf R}$ is located, extending results presented recently by F. Richman and H. Ishihara for subsets of a Hilbert space.References
- Errett Bishop, Foundations of constructive analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221878
- Errett Bishop and Douglas Bridges, Constructive analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 279, Springer-Verlag, Berlin, 1985. MR 804042, DOI 10.1007/978-3-642-61667-9
- Douglas Bridges and Fred Richman, Varieties of constructive mathematics, London Mathematical Society Lecture Note Series, vol. 97, Cambridge University Press, Cambridge, 1987. MR 890955, DOI 10.1017/CBO9780511565663
- Luminiţa Dediu (Vîţă), The Constructive Theory of Operator Algebras, Ph.D. Thesis, University of Canterbury, New Zealand, 2000.
- Hajime Ishihara, On the constructive Hahn-Banach theorem, Bull. London Math. Soc. 21 (1989), no. 1, 79–81. MR 967795, DOI 10.1112/blms/21.1.79
- Hajime Ishihara, Locating subsets of a Hilbert space, Proc. Amer. Math. Soc. 129 (2001), no. 5, 1385–1390. MR 1712901, DOI 10.1090/S0002-9939-00-05674-4
- D. L. Johns and C. G. Gibson, A constructive approach to the duality theorem for certain Orlicz spaces, Math. Proc. Cambridge Philos. Soc. 89 (1981), no. 1, 49–69. MR 591972, DOI 10.1017/S0305004100057947
- Fred Richman, Adjoints and the image of the ball, Proc. Amer. Math. Soc. 129 (2001), no. 4, 1189–1193. MR 1701689, DOI 10.1090/S0002-9939-00-05618-5
- Wataru Takahashi, Nonlinear functional analysis, Yokohama Publishers, Yokohama, 2000. Fixed point theory and its applications. MR 1864294
Additional Information
- Hajime Ishihara
- Affiliation: School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan
- Email: ishihara@jaist.ac.jp
- Luminiţa Vîţă
- Affiliation: Department of Mathematics and Statistics, Private Bag 4800, University of Canterbury, New Zealand
- Email: luminita@math.net
- Received by editor(s): April 19, 2002
- Published electronically: March 11, 2003
- Additional Notes: The authors were partly supported by a Grant-in-Aid for Scientific Research (C) No. 09640253 of the Ministry of Education, Science, Sports and Culture of Japan
- Communicated by: Jonathan M. Borwein
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3231-3239
- MSC (2000): Primary 03F60, 46S30
- DOI: https://doi.org/10.1090/S0002-9939-03-07067-9
- MathSciNet review: 1992864