On the fixed point property in direct sums of Banach spaces with strictly monotone norms
Volume 186 / 2008
Studia Mathematica 186 (2008), 87-99
MSC: Primary 47H09, 47H10; Secondary 46B20.
DOI: 10.4064/sm186-1-8
Abstract
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 $Y$ has the asymptotic (P) property (which is weaker than the condition ${\rm WCS}( Y) >1$), then $X\oplus Y$ endowed with a strictly monotone norm enjoys the weak fixed point property. The same conclusion is valid if $X$ admits a $1$-unconditional basis.
