Tsirelson-like spaces and complexity of classes of Banach spaces

Abstract

Employing a construction of Tsirelson- like spaces due to Argyros and Deliyanni, we show that the class of all Banach spaces which are isomorphic to a subspace of c0 is a complete analytic set with respect to the Effros Borel structure of separable Banach spaces. Moreover, the classes of all separable spaces with the Schur property and of all separable spaces with the Dunford- Pettis property are Pi 12-complete.

Keywords

• Effros Borel structure
• Complete analytic set
• Tsirelson space
• Banach space c(0)
• Schur property