Smooth extensions of functions on separable Banach spaces

Details Smooth extensions of functions on separable Banach spaces Smooth extensions of functions on separable Banach spaces

2009-06-16

arxiv.org/abs/0906.2989v2

Mathematics

Functional Analysis

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

Scientific paper

Let $X$ be a Banach space with a separable dual $X^{*}$. 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 $X$.

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