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

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

2007-06-06

arxiv.org/abs/0706.0915v2

Studia Mathematica 186 (2008), 87--99

Mathematics

Functional Analysis

corrected and extended version, 13 pages

Scientific paper

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.

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