Geodesic
Some topics on the continuation and smoothing of vector functions
Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 906-916

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider problems of continuation of vector functions from a subspace to the entire space and of smoothing problems for these functions. It is shown that there exists a reflexive separable space $X$ and a subspace $Y$ such that even a very smooth mapping of $Y$ does not extend to a uniformly continuous mapping of a neighborhood of $Y$. 
@article{MZM_1995_58_6_a9,
     author = {I. G. Tsar'kov},
     title = {Some topics on the continuation and smoothing of vector functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {906--916},
     publisher = {mathdoc},
     volume = {58},
     number = {6},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a9/}
}
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I. G. Tsar'kov. Some topics on the continuation and smoothing of vector functions. Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 906-916. http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a9/