Abstract
We show that the set of all separable Banach spaces that have the π-property is a Borel subset of the set of all closed subspaces of C(Δ), where Δ is the Cantor set, equipped with the standard Effros-Borel structure. We show that if α < ω 1, the set of spaces with Szlenk index at most α which have a shrinking FDD is Borel.
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Ghawadrah, G. The descriptive complexity of the family of Banach spaces with the π-property. Arab.J.Math. 4, 35–39 (2015). https://doi.org/10.1007/s40065-014-0116-3
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DOI: https://doi.org/10.1007/s40065-014-0116-3