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arXiv:0906.2989 [math.FA]AbstractReferencesReviewsResources

Smooth extensions of functions on separable Banach spaces

D. Azagra, R. Fry, L. Keener

Published 2009-06-16, updated 2010-01-28Version 2

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 $X$.

Comments: 19 pages. This version fixes a gap in the previous proof of Theorem 1 by providing a sharp version of Lemma 1
Categories: math.FA
Subjects: 46B20
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