English

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