Smooth extensions of functions on separable Banach spaces

Abstract

Let $X$ be a Banach space with a separable dual $X^{\ast }$. Let $Y\subset X$ be a closed subspace, and $f:Y\to \mathbb{R}$ a $C^1$-smooth function. Then we show there is a $C^1$ extension of $f$ to $X$.

19 pages. This version fixes a gap in the previous proof of Theorem 1 by providing a sharp version of Lemma 1

Cited by in corpus (1)

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