Non-universal families of separable Banach spaces

Ondřej Kurka. "Non-universal families of separable Banach spaces." Studia Mathematica 233.2 (2016): 153-168. <http://eudml.org/doc/285913>.

@article{OndřejKurka2016,
abstract = {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.},
author = {Ondřej Kurka},
journal = {Studia Mathematica},
keywords = {isometrically universal Banach space; Effros Borel structure; analytic set; monotone basis; strict convexity},
language = {eng},
number = {2},
pages = {153-168},
title = {Non-universal families of separable Banach spaces},
url = {http://eudml.org/doc/285913},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Ondřej Kurka
TI - Non-universal families of separable Banach spaces
JO - Studia Mathematica
PY - 2016
VL - 233
IS - 2
SP - 153
EP - 168
AB - 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.
LA - eng
KW - isometrically universal Banach space; Effros Borel structure; analytic set; monotone basis; strict convexity
UR - http://eudml.org/doc/285913
ER -