Differentiable functions and rough norms on Banach spaces

Leach, E. B.; Whitfield, J. H. M.

doi:10.1090/S0002-9939-1972-0293394-4

Differentiable functions and rough norms on Banach spaces
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by E. B. Leach and J. H. M. Whitfield PDF

Proc. Amer. Math. Soc. 33 (1972), 120-126 Request permission

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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