Amalgamations of classes of Banach spaces with a monotone basis

Volume 234 / 2016

Ondřej Kurka Studia Mathematica 234 (2016), 121-148 MSC: Primary 46B04, 54H05; Secondary 46B15, 46B20, 46B70. DOI: 10.4064/sm8281-7-2016 Published online: 23 August 2016


It was proved by Argyros and Dodos that, for many classes $ \mathcal {C} $ of separable Banach spaces which share some property $ P $, there exists an isomorphically universal space that satisfies $ P $ as well. We introduce a variant of their amalgamation technique which provides an isometrically universal space in the case that $ \mathcal {C} $ consists of spaces with a monotone Schauder basis. For example, we prove that if $ \mathcal {C} $ is a set of separable Banach spaces which is analytic with respect to the Effros Borel structure and every $ X \in \mathcal {C} $ is reflexive and has a monotone Schauder basis, then there exists a separable reflexive Banach space that is isometrically universal for $ \mathcal {C} $.


  • Ondřej KurkaDepartment of Mathematical Analysis
    Charles University
    Sokolovská 83
    186 75 Praha 8, Czech Republic

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