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Abstract

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} $.