Two applications of smoothness in $C(K)$ spaces
Studia Mathematica, Tome 225 (2014) no. 1, pp. 1-7
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A simple observation about embeddings of smooth Banach spaces into $C(K)$ spaces allows us to construct a parametrization of the separable Banach spaces using closed subsets of the interval $[0,1]$. The same idea is applied to the study of the isometric embedding of $\ell _p$ spaces into certain $C(K)$ spaces with the additional condition that the functions of the image must be Lipschitz with respect to a fixed finer metric
on $K$. The feasibility of that kind of embeddings is related to Szlenk indices.
Keywords:
simple observation about embeddings smooth banach spaces spaces allows construct parametrization separable banach spaces using closed subsets interval idea applied study isometric embedding ell spaces certain spaces additional condition functions image lipschitz respect fixed finer metric nbsp feasibility kind embeddings related szlenk indices
Affiliations des auteurs :
Matías Raja 1
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author = {Mat{\'\i}as Raja},
title = {Two applications of smoothness in $C(K)$ spaces},
journal = {Studia Mathematica},
pages = {1--7},
publisher = {mathdoc},
volume = {225},
number = {1},
year = {2014},
doi = {10.4064/sm225-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm225-1-1/}
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Matías Raja. Two applications of smoothness in $C(K)$ spaces. Studia Mathematica, Tome 225 (2014) no. 1, pp. 1-7. doi: 10.4064/sm225-1-1
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