The fixed point property for subsets of some classical Banach spaces (Q1348733)

In a previous paper [Proc. Am. Math. Soc. 125, No. 2, 443-446 (1997; Zbl 0861.47032)], the first two authors proved that nonreflexive subspaces of \(L_1\) fail to have the fixed point property. Here, the authors prove that, given a closed bounded convex subset \(K\) of a Banach space which contains an asymptotically isometric \(\ell^1\)-basis, one may find a closed convex set \(C\subseteq K\) and a fixed point free nonexpansive affine map \(T: C\to C\).