We prove that if 𝓒 is a family of separable Banach spaces which is analytic with respect to the Effros Borel structure and no X ∈ 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 𝓒 but not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8380-4-2016,
author = {Ond\v rej Kurka},
title = {Non-universal families of separable Banach spaces},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {153-168},
zbl = {06586873},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8380-4-2016}
}
Ondřej Kurka. Non-universal families of separable Banach spaces. Studia Mathematica, Tome 233 (2016) pp. 153-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8380-4-2016/