This is an announcement for the paper “On the fixed point property in Banach spaces isomorphic to $c_0$” by Cleon S. Barrosohttps://arxiv.org/search/math?searchtype=author&query=Barroso%2C+C+S.

Abstract: We prove that every Banach space containing a subspace isomorphic to $\co$ fails the fixed point property. The proof is based on an amalgamation approach involving a suitable combination of known results and techniques, including James's distortion theorem, Ramsey's combinatorial theorem, Brunel-Sucheston spreading model techniques and Dowling, Lennard and Turett's fixed point methodology employed in their characterization of weak compactness in $\co$.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1807.11614