Properties WORTH and WORTH\(^*\), \((1+\delta)\) embeddings in Banach spaces with 1-unconditional basis and wFPP
The authors show that a Banach space \(X\) that \((1+\delta)\) embeds in a subspace \(X_\delta\) of a Banach space \(Y\) with a \(1\)-unconditional basis has the weak fixed point property for nonexpansive mappings. In fact, such a space has the property AMC introduced by \textit{J. García Falset} and \textit{E. Lloréns-Fuster} [J. Math. Anal. Appl. 172, No.~1, 39--52 (1993; Zbl 0780.47039)]. Applying this to the result proved by \textit{S. R. Cowell} and \textit{N. J. Kalton} [Q. J. Math. 61, No.~2, 217--240 (2010; Zbl 1215.46010)], they can show that if \(X\) is a reflexive Banach space and has the property WORTH, then \(X\) and its dual \(X^*\) have the fixed point property for nonexpansive mappings.
scientific article; zbMATH DE number 5692322