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Every separable Banach space is isometric to a space of continuous nowhere differentiable functions. (English) Zbl 0844.46007
Summary: We prove the result stated in the title; that is, every separable Banach space is linearly isometric to a closed subspace $$E$$ of the space of continuous functions on $$[0,1 ]$$, such that every nonzero function in $$E$$ is nowhere differentiable.

##### MSC:
 46B04 Isometric theory of Banach spaces 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
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