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arXiv · 1504.06862

Amalgamations of classes of Banach spaces with a monotone basis

Ondřej Kurka
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Abstract

It was proved by Argyros and Dodos that, for many classes $ 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 $ C $ consists of spaces with a monotone Schauder basis. For example, we prove that if $ C $ is a set of separable Banach spaces which is analytic with respect to the Effros-Borel structure and every $ X \in C $ is reflexive and has a monotone Schauder basis, then there exists a separable reflexive Banach space that is isometrically universal for $ C $.

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Ondřej Kurka. 2015-04-26. Amalgamations of classes of Banach spaces with a monotone basis. https://doi.org/10.4064/sm8281-7-2016

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