On the fixed points of nonexpansive mappings in direct sums of Banach spaces
Tom 207 / 2011
Studia Mathematica 207 (2011), 75-84 MSC: 47H10, 46B20, 47H09. DOI: 10.4064/sm207-1-5
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.