On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces

2011/12/26 by M. J. Sevilla, Jimenez-Sevilla, M., Luis Sánchez-González +1 · 1 citation
Mathematics · #46B20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.1112.5888

openalex publication_date 2011/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X and Z be Banach spaces, A a closed subset of X and a mapping f:A → Z. We give necessary and sufficient conditions to obtain a C¹ smooth mapping F:X → Z such that F_|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=L₂ and Z=L_p with 1

Citations

• On the complemented subspaces problem

Cited by

• On Whitney-type extension theorems for C^1,+, C², C^2,+, and C³-smooth mappings between Banach spaces

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