Differentiable functions and rough norms on Banach spaces-Reference-Cited by-同舟云学术

Differentiable functions and rough norms on Banach spaces

Published:1972 Issue:1 Volume:33 Page:120-126
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

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

Abstract

The main result is that if X is a real Banach space, such that the density character of X ∗ {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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-033-01/S0002-9939-1972-0293394-4/S0002-9939-1972-0293394-4.pdf

Reference7 articles.

1. Differentiable functions on certain Banach spaces;Bonic, Robert;Bull. Amer. Math. Soc.,1965

2. Conditions for the differentiability of a norm in a Banach space;Kadec′, M. Ĭ.;Uspehi Mat. Nauk,1965

3. On approximation in real Banach spaces;Kurzweil, J.;Studia Math.,1954

4. Differentiable norms in Banach spaces;Restrepo, Guillermo;Bull. Amer. Math. Soc.,1964

5. Differentiable norms;Restrepo, Guillermo;Bol. Soc. Mat. Mexicana (2),1965

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