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Differentiable Functions and Rough Norms on Banach Spaces
E. B. Leach and J. H. M. Whitfield
Proceedings of the American Mathematical Society
Vol. 33, No. 1 (May, 1972), pp. 120-126
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2038183
Page Count: 7
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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.
Proceedings of the American Mathematical Society © 1972 American Mathematical Society