This is an announcement for the paper "On the fixed points of nonexpansive mappings in direct sums of Banach spaces" by Andrzej Wisnicki.

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 a direct sum of X and Y, with respect to a strictly monotone norm, has the weak fixed point property. The result is new even if Y is a finite-dimensional space.

Archive classification: math.FA

Remarks: 9 pages. To appear, Studia Mathematica

Submitted from: awisnic@golem.umcs.lublin.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1111.6965

or

http://arXiv.org/abs/1111.6965