Smooth extensions of functions on separable Banach spaces

2009/06/16 by D. Azagra, Azagra, D., R. Fry +3
Mathematics · #46B20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B20

paper · pdf · doi:10.48550/arxiv.0906.2989

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

arxiv created 2010/01/28 · arxiv updated 2010/02/08

Abstract

Let X be a Banach space with a separable dual X^*. Let Y⊂ X be a closed subspace, and f:Y→ℝ a C¹-smooth function. Then we show there is a C¹ extension of f to X.

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