The property WORTH* and the weak fixed point property

Dalby, Tim (2014) The property WORTH* and the weak fixed point property. Journal of Nonlinear and Convex Analysis, 15 (5). pp. 919-927. ISSN 1345-4773

Abstract

A Banach space, $X$, has the weak fixed point property (w-FPP) if every nonexpansive mapping, $T$, on every weak compact convex nonempty subset, $C$, has a fixed point. A Banach space, $X^*$, has WORTH* if for every weak* null sequence $(x^*_n)$ and every $x^* \in X^*$,

$\limsup_n\|x^*_n-x^*\|=\limsup_n\|x^*_n+x^*\|.$

A new proof is given of the recent result that WORTH* implies the weak fixed point property.

Item Type: Article (Commonwealth Reporting Category C) Yes Live Archive © 2014 Yokohama Publishing. Permanent restricted access to paper in accordance with the copyright policy of the publisher. Current - Open Access College 10 Aug 2014 06:10 18 Oct 2017 02:40 properties WORTH; WORTH*; weak fixed point property; 1-unconditional basis 01 Mathematical Sciences > 0101 Pure Mathematics > 010108 Operator Algebras and Functional Analysis01 Mathematical Sciences > 0105 Mathematical Physics > 010501 Algebraic Structures in Mathematical Physics E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences http://eprints.usq.edu.au/id/eprint/25705