This is an announcement for the paper “A Bourgain-like property of Banach spaces with no copies of $c_0$” by A. Perez and M Raja.

Abstract: We give a characterization of the existence of copies of $c_0$ in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessaga-Pelczynski theorem about weakly unconditionally Cauchy series.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.08706