Construction of pathological Gâteaux differentiable functions

Deville, Robert; Ivanov, Milen; Lajara, Sebastián

doi:10.1090/S0002-9939-2014-12206-4

Construction of pathological Gâteaux differentiable functions
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by Robert Deville, Milen Ivanov and Sebastián Lajara PDF

Proc. Amer. Math. Soc. 143 (2015), 129-139 Request permission

Abstract:

We prove that for many pairs $(X,Y)$ of classical Banach spaces, there exists a bounded, Lipschitz, Gâteaux differentiable function from $X$ to $Y$ whose derivatives are all far apart.

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