On the fixed points of nonexpansive mappings in direct sums of Banach spaces
Functional Analysis
2015-11-24 v1
Abstract
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 of X and Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
Keywords
Cite
@article{arxiv.1111.6965,
title = {On the fixed points of nonexpansive mappings in direct sums of Banach spaces},
author = {Andrzej Wiśnicki},
journal= {arXiv preprint arXiv:1111.6965},
year = {2015}
}
Comments
9 pages. To appear, Studia Mathematica