an equivalent norm on X that fails to be Fréchet differentiable at every point of X. In 1976, Ekeland & Lebourg showed that if X is a Banach space that has an equivalent norm that is Fréchet differentiable away from the origin, then X is an Asplund space. However, in 1990, Haydon gave an example of an Asplund space that does not have an equivalent norm that is Gateaux differentiable away from the origin. References Banach spaces Functional analysis