Some renormings with the stable fixed point property

Abstract

In this paper, we prove that for any number λ < (√33−3)/2, any separable space X can be renormed in such a way that X satisfies the weak fixed point property for non-expansive mappings and this property is inherited for any other isomorphic space Y such that the Banach-Mazur distance between X and Y is less than λ. We also prove that any, in general nonseparable, Banach space with an extended unconditional basis can be renormed to satisfy the w-FPP with the same stability constant.