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A remark on bases and reflexivity in Banach spaces

Israel Journal of Mathematics volume 6, pages 74–79 (1968)Cite this article

Abstract

LetX be a Banach space with a basis. It is proved that if (a) all bases ofX are shrinking, or (b) all bases ofX are boundedly complete, thenX is reflexive.

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References

  1. M. M. Day,Normed linear spaces, Springer, 1958.

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Authors and Affiliations

  1. The Hebrew University of Jerusalem, Israel

    M. Zippin

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  1. M. Zippin
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Additional information

Research supported by Grant AF EOAR 66-18.

This is part of the author’s Ph.D. thesis prepared at The Hebrew University of Jerusalem, under the supervision of Professor A. Dvoretzky and Professor J. Lindenstrauss. The author wishes to thank Professor Lindenstrauss for his valuable remarks.

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Zippin, M. A remark on bases and reflexivity in Banach spaces. Israel J. Math. 6, 74–79 (1968). https://doi.org/10.1007/BF02771607

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  • DOI: https://doi.org/10.1007/BF02771607

Keywords

  • Banach Space
  • Nonnegative Integer
  • Dimensional Subspace
  • Basic Sequence
  • Studia Math