The fixed point property in $\lowercase{c_0}$

http://dx.doi.org/10.4153/CMB-1998-055-2
Canad. Math. Bull. 41(1998), 413-422

  Published:1998-12-01
 Printed: Dec 1998

A closed convex subset of $c_0$ has the fixed point property ($\fpp$) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of $c_0$ are known to have the $\fpp$. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the $\fpp$.