On the fixed point property in Banach spaces isomorphic to $c_0$

TL;DR

This paper demonstrates that Banach spaces containing a subspace isomorphic to c0 do not have the fixed point property, using a combination of classical and modern techniques in functional analysis.

Contribution

It introduces a new proof that Banach spaces with a c0 subspace lack the fixed point property, integrating several advanced methods in the field.

Findings

Banach spaces with a c0 subspace fail the fixed point property

The proof combines James's distortion theorem and Ramsey's theorem

Utilizes spreading model techniques and fixed point characterizations

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 $\co$.