We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum X ⊕ Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-5,
author = {Andrzej Wi\'snicki},
title = {On the fixed points of nonexpansive mappings in direct sums of Banach spaces},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {75-84},
zbl = {1252.47061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-5}
}
Andrzej Wiśnicki. On the fixed points of nonexpansive mappings in direct sums of Banach spaces. Studia Mathematica, Tome 204 (2011) pp. 75-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-5/