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W2013313441 abstract "Let $$X$$ and $$ Z$$ be Banach spaces, $$A$$ a closed subset of $$X$$ and a mapping $$f:Arightarrow Z$$ . We give necessary and sufficient conditions to obtain a $$C^1$$ smooth mapping $$F:X rightarrow Z$$ such that $$F_{mid _A}=f$$ , when either (i) $$X$$ and $$Z$$ are Hilbert spaces and $$X$$ is separable, or (ii) $$X^*$$ is separable and $$Z$$ is an absolute Lipschitz retract, or (iii) $$X=L_2$$ and $$Z=L_p$$ with $$1<p<2$$ , or (iv) $$X=L_p$$ and $$Z=L_2$$ with $$2<p<infty $$ , where $$L_p$$ is any separable Banach space $$L_p(S,Sigma ,mu )$$ with $$(S,Sigma ,mu )$$ a $$sigma $$ -finite measure space." @default.
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W2013313441 date "2012-05-17" @default.
W2013313441 modified "2023-10-14" @default.
W2013313441 title "On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces" @default.
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W2013313441 doi "https://doi.org/10.1007/s00208-012-0814-0" @default.
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