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The Banach-Saks Theorem in C(S)

Published online by Cambridge University Press:  20 November 2018

Nicholas R. Farnum
Nicholas R. Farnum*
Affiliation:
University of California, Irvine, Irvine, California
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A Banach space X has the Banach-Saks property if every sequence (xn) in X converging weakly to x has a subsequence (xnk) with (1/p)Σk=1xnk converging in norm to x. Originally, Banach and Saks [2] proved that the spaces Lp (p > 1) have this property. Kakutani [4] generalized their result by proving this for every uniformly convex Banach space, and in [9] Szlenk proved that the space L1 also has this property.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 91 - 97
Copyright
Copyright © Canadian Mathematical Society 1974

References

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