Non-universal families of separable Banach spaces
Studia Mathematica, Tome 233 (2016) no. 2, pp. 153-168
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We prove that if $ \mathcal {C} $ is a family of separable Banach spaces which is analytic with respect to the Effros Borel structure and no $ X \in \mathcal {C} $ is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for $ \mathcal {C} $ but not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.
Keywords:
prove mathcal family separable banach spaces which analytic respect effros borel structure mathcal isometrically universal separable banach spaces there exists separable banach space monotone schauder basis which isometrically universal mathcal separable banach spaces establish analogous result class strictly convex spaces
Affiliations des auteurs :
Ondřej Kurka 1
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author = {Ond\v{r}ej Kurka},
title = {Non-universal families of separable {Banach} spaces},
journal = {Studia Mathematica},
pages = {153--168},
year = {2016},
volume = {233},
number = {2},
doi = {10.4064/sm8380-4-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8380-4-2016/}
}
Ondřej Kurka. Non-universal families of separable Banach spaces. Studia Mathematica, Tome 233 (2016) no. 2, pp. 153-168. doi: 10.4064/sm8380-4-2016
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