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On the Banach–Saks property

Published online by Cambridge University Press:  24 October 2008

J. R. Partington
J. R. Partington
Affiliation:
Trinity College, Cambridge CB2 1TQ
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Extract

A Banach space X is said to have the Banach–Saks property (BS) if every bounded sequence (xn) in X has a subsequence (), which is (C, 1) convergent in norm to a point x in X; that is,

Kakutani (7) showed that all uniformly convex spaces are (BS); moreover, all (BS) spaces are reflexive. It is further known that both these implicationsare strict: see, for example, Baernstein (1) and Diestel (4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 3 , November 1977 , pp. 369 - 374
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

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