Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 342691, 7 pages
Research Article

Properties WORTH and WORTHH, (1+δ) Embeddings in Banach Spaces with 1-Unconditional Basis and wFPP

Centro de Investigación en Matemáticas (CIMAT), Apdo. Postal 402, 36000 Guanajuato, GTO, Mexico

Received 24 September 2009; Accepted 3 November 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Helga Fetter and Berta Gamboa de Buen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We will use García-Falset and Lloréns Fuster's paper on the AMC-property to prove that a Banach space X that (1+δ) embeds in a subspace Xδ of a Banach space Y with a 1-unconditional basis has the property AMC and thus the weak fixed point property. We will apply this to some results by Cowell and Kalton to prove that every reflexive real Banach space with the property WORTH and its dual have the FPP and that a real Banach space X such that BX is w sequentially compact and X has WORTH has the wFPP.