This is an announcement for the paper "On the complexity of some classes of Banach spaces and" by Bruno de Mendonca Braga.

Abstract: These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the LUST property. We also show that the weak Banach-Saks property, the Schur property, the Dunford-Pettis property, the analytic Radon-Nikodym property, the set of Banach spaces whose set of unconditionally converging operators is complemented in its bounded oper- ators, the set of Banach spaces whose set of weakly compact operators is complemented in its bounded operators, and the set of Banach spaces whose set of Banach-Saks opera- tors is complemented in its bounded operators, are all non Borel in SB. At last, we give several applications of those results to non-universality results.

Archive classification: math.FA

Submitted from: demendoncabraga@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1508.01960

or

http://arXiv.org/abs/1508.01960