Uniform differentiability, compactness, and 𝑙¹

Bilyeu, Russell G.; Lewis, Paul W.

doi:10.1090/S0002-9939-1986-0831393-1

Uniform differentiability, compactness, and $l^ 1$
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by Russell G. Bilyeu and Paul W. Lewis

Proc. Amer. Math. Soc. 97 (1986), 87-92

DOI: https://doi.org/10.1090/S0002-9939-1986-0831393-1

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Abstract:

In an earlier paper the authors have shown that conditionally compact subsets of ${l^1}$ are characterized by uniform Gâteaux differentiability. Results in this paper show that this equivalence characterizes spaces which contain ${l^1}$.

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