Smooth functions onc 0
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We show that every Fréchet differentiable real function onc 0 with locally uniformly continuous derivative has locally compact derivative. Among the corollaries we obtain that there exists no surjectiveC 2 smooth operator fromc 0 onto an infinite dimensional space with nontrivial type.
KeywordsBanach Space Continuous Derivative Infinite Dimensional Space Separable Subspace Disjoint Block
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