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A remark on bases and reflexivity in Banach spaces


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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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).

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