On the fixed point property in direct sums of Banach spaces with strictly monotone norms

Stanisław Prus, Andrzej Wiśnicki

Published 2007-06-06, updated 2007-11-14Version 2

It is shown that if a Banach space X has the weak Banach-Saks property and the weak fixed point property for nonexpansive mappings and Y satisfies property asymptotic (P) (which is weaker than the condition WCS(Y)>1), then the direct sum of X and Y endowed with a strictly monotone norm enjoys the weak fixed point property. The same conclusion is valid if X admits a 1-unconditional basis.