Non-universal families of separable Banach spaces
Volume 233 / 2016
Studia Mathematica 233 (2016), 153-168
MSC: Primary 46B04, 54H05; Secondary 46B15, 46B20, 46B25.
DOI: 10.4064/sm8380-4-2016
Published online: 20 May 2016
Abstract
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.
