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

 

Differentiable functions and rough norms on Banach spaces


Authors: E. B. Leach and J. H. M. Whitfield
Journal: Proc. Amer. Math. Soc. 33 (1972), 120-126
MSC: Primary 46G05; Secondary 47B99
MathSciNet review: 0293394
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Abstract: The main result is that if X is a real Banach space, such that the density character of $ {X^\ast}$ is greater than that of X, then there does not exist any real-valued Fréchet differentiable function on X with bounded nonempty support.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0293394-4
PII: S 0002-9939(1972)0293394-4
Keywords: Fréchet differential, Gâteaux differential, one-sided Gâteaux differential, uniformly discontinuous, rough norm, density character, large set, bounded nonempty support
Article copyright: © Copyright 1972 American Mathematical Society