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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Constructive reflexivity of a uniformly convex Banach space
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by Hajime Ishihara PDF
Proc. Amer. Math. Soc. 104 (1988), 735-740 Request permission

Abstract:

In this paper we consider a question about reflexivity of a Banach space within the framework of Bishop’s constructive mathematics and we give a partially affirmative answer to the question set by Bishop: "Is every uniformly convex Banach space reflexive?".
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 S. Bridges, Constructive functional analysis, Research Notes in Mathematics, vol. 28, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR 521982
  • 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
  • H. Ishihara, On the constructive Hahn-Banach theorem, submitted.
  • Ronald Larsen, Functional analysis: an introduction, Pure and Applied Mathematics, No. 15, Marcel Dekker, Inc., New York, 1973. MR 0461069
  • K. Yoshida, Functional analysis, Springer-Verlag, Berlin, 1968.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 104 (1988), 735-740
  • MSC: Primary 46R05; Secondary 03F65, 46B10
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0964849-3
  • MathSciNet review: 964849