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Locating subsets of a normed space

Authors: Hajime Ishihara and Luminita Vita
Journal: Proc. Amer. Math. Soc. 131 (2003), 3231-3239
MSC (2000): Primary 03F60, 46S30
Published electronically: March 11, 2003
MathSciNet review: 1992864
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Errett Bishop, Foundations of Constructive Analysis, New York, McGraw Hill, 1967. MR 36:4930
  • 2. Errett Bishop, Douglas Bridges, Constructive Analysis, Springer-Verlag Berlin Heidelberg, 1985. MR 87d:03172
  • 3. Douglas Bridges, Fred Richman, Varieties of Constructive Mathematics, Cambridge University Press, 1987. MR 88k:03127
  • 4. Luminita Dediu (Vîta), The Constructive Theory of Operator Algebras, Ph.D. Thesis, University of Canterbury, New Zealand, 2000.
  • 5. Hajime Ishihara, On the constructive Hahn-Banach theorem, Bull. London Math. Soc. 21(1989), 79-81. MR 90a:46197
  • 6. Hajime Ishihara, Locating subsets of a Hilbert space, Proc. Amer. Math. Soc. 129 no. 5 (2001), 1385-1390. MR 2001h:46132
  • 7. D. Johns and C. Gibson, A constructive approach to the duality theorem for certain Orlicz spaces, Math. Proc. Cambridge Philos. Soc. 89(1981), 49-69. MR 81m:46046
  • 8. Fred Richman, Adjoints and the image of the ball, Proc. Amer. Math. Soc. 129(2001), 1189-1193. MR 2001g:47002
  • 9. Wataru Takahashi, Nonlinear functional analysis, Yokohama Publishers, 2000. MR 2002k:47001

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Additional Information

Hajime Ishihara
Affiliation: School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan

Luminita Vita
Affiliation: Department of Mathematics and Statistics, Private Bag 4800, University of Canterbury, New Zealand

Keywords: Functional analysis, constructive mathematics.
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
Article copyright: © Copyright 2003 American Mathematical Society

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