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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniform differentiability, compactness, and $ l\sp 1$


Authors: Russell G. Bilyeu and Paul W. Lewis
Journal: Proc. Amer. Math. Soc. 97 (1986), 87-92
MSC: Primary 46B05; Secondary 46B20, 46B25, 46G05
MathSciNet review: 831393
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0831393-1
PII: S 0002-9939(1986)0831393-1
Keywords: Uniform Gâteaux differentiability, Day's norm on $ {c_0}$, maximal monotone operator, conditional compactness, isomorphic copy of $ {l^1}$
Article copyright: © Copyright 1986 American Mathematical Society