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The Banach-Saks Theorem in C(S)
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1974
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