On the fixed points of nonexpansive mappings in direct sums of Banach spaces
Volume 207 / 2011
Studia Mathematica 207 (2011), 75-84
MSC: 47H10, 46B20, 47H09.
DOI: 10.4064/sm207-1-5
Abstract
We show that if a Banach space $X$ has the weak fixed point property for nonexpansive mappings and $Y$ has the generalized Gossez–Lami Dozo property or is uniformly convex in every direction, then the direct sum $X\oplus Y$ with a strictly monotone norm has the weak fixed point property. The result is new even if $Y$ is finite-dimensional.
