A Bourgain-like property of Banach spaces with no copies of $c_0$

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-Pełczynski theorem about weakly unconditionally Cauchy series.

To appear in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas