Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 342691, 7 pages
doi:10.1155/2010/342691

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

Abstract

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.