Unconditional bases and fixed points of nonexpansive mappings
Using Maurey's ultraproduct techniques, the author has proved the following two theorems: Theorem 1. Let X be a Banach space with an unconditional basis. If the unconditional constant \(\lambda <(\sqrt{33}-3)/2\), then every weakly compact convex subset of X has the fixed point property for nonexpansive mappings. Theorem 2. Let X be a superreflexive space with a suppression unconditional basis. Then every weakly compact convex subset of X has the fixed point property for nonexpansive mappings. But the following problem is still open: Problem. Let X be a (superreflexive) Banach space with an unconditional basis. Does every weakly compact convex subset of X have the fixed point property for nonexpansive mappings?
Banach space with an unconditional basis
fixed point property for nonexpansive mappings
superreflexive space with a suppression unconditional basis
scientific article; zbMATH DE number 3903393