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arXiv · 0706.0915

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

Stanisław Prus·Andrzej Wiśnicki
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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 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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Stanisław Prus, Andrzej Wiśnicki. 2007-06-06. On the fixed point property in direct sums of Banach spaces with strictly monotone norms. https://doi.org/10.4064/sm186-1-8

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