This is an announcement for the paper "Amalgamations of classes of Banach spaces with a monotone basis" by Ondrej Kurka.

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 $.

Archive classification: math.FA

Mathematics Subject Classification: 46B04, 54H05 (Primary) 46B15, 46B20, 46B70 (Secondary)

Submitted from: kurka.ondrej@seznam.cz

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1504.06862

or

http://arXiv.org/abs/1504.06862