Amalgamations of classes of Banach spaces with a monotone basis

Ondřej Kurka ¹

¹ Department of Mathematical Analysis Charles University Sokolovská 83 186 75 Praha 8, Czech Republic

Studia Mathematica, Tome 234 (2016) no. 2, pp. 121-148

Résumé

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} $.

Détail

DOI : 10.4064/sm8281-7-2016

Keywords: proved argyros dodos many classes mathcal separable banach spaces which share property there exists isomorphically universal space satisfies introduce variant their amalgamation technique which provides isometrically universal space mathcal consists spaces monotone schauder basis example prove mathcal set separable banach spaces which analytic respect effros borel structure every mathcal reflexive has monotone schauder basis there exists separable reflexive banach space isometrically universal mathcal