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Proceedings of the American Mathematical Society

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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: 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.

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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