Fixed point property for general topologies in some Banach spaces

Abstract

We study the fixed point property with respect to general vector topologies in L-embedded Banach spaces. Considering a class of topologies in l1 such that the standard basis is convergent, we characterise those of them for which the fixed point property holds. We show that in c0-sums of some Banach spaces the weak topology is in a sense the coarsest topology for which the fixed point property holds.