On unconditionally saturated Banach spaces

Pandelis Dodos¹ ; Jordi Lopez-Abad²

¹ Équipe d'Analyse Fonctionnelle Université Pierre et Marie Curie – Paris 6 Boîte 186 4 place Jussieu 75252 Paris Cedex 05, France
² Équipe de Logique Mathématiques Université Denis Diderot – Paris 7 2 place Jussieu 72521 Paris Cedex 05, France

Studia Mathematica, Tome 188 (2008) no. 2, pp. 175-191

Résumé

We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set $\mathcal{A}$, in the Effros–Borel space of subspaces of $C[0,1]$, of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space $Y$, with a Schauder basis, that contains isomorphic copies of every space $X$ in the class $\mathcal{A}$.

Détail

DOI : 10.4064/sm188-2-5

Keywords: prove structural property class unconditionally saturated separable banach spaces particular every analytic set mathcal effros borel space subspaces unconditionally saturated separable banach spaces there exists unconditionally saturated banach space schauder basis contains isomorphic copies every space class mathcal