On unconditionally saturated Banach spaces
Volume 188 / 2008
Studia Mathematica 188 (2008), 175-191
MSC: Primary 46B03, 46B15; Secondary 03E15, 46B07.
DOI: 10.4064/sm188-2-5
Abstract
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 $\mathcal{A}$.
