tailieunhanh - Báo cáo hóa học: " Research Article Properties WORTH and WORTHH∗ , 1 δ Embeddings in Banach Spaces with 1-Unconditional Basis and wFPP"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Properties WORTH and WORTHH∗ , 1 δ Embeddings in Banach Spaces with 1-Unconditional Basis and wFPP | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 342691 7 pages doi 2010 342691 Research Article Properties WORTH and WORTHH 1 6 Embeddings in Banach Spaces with 1-Unconditional Basis and wFPP Helga Fetter and Berta Gamboa de Buen Centro de Investigation en Matemdticas CIMAT Apdo. Postal 402 36000 Guanajuato GTO Mexico Correspondence should be addressed to Helga Fetter fetter@ Received 24 September 2009 Accepted 3 November 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 H. Fetter and B. 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 Garcia-Falset and Llorens Fuster s paper on the AMC-property to prove that a Banach space X that 1 6 embeds in a subspace Xfi 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. 1. Introduction In 1988 Sims 1 introduced the notion of weak orthogonality WORTH and asked whether spaces with WORTH have the weak fixed point property wFPP . Since then several partial answers have been given. For instance in 1993 Garcia-Falset 2 proved that if X is uniformly nonsquare and has WORTH then it has the wFPP although Mazcunan Navarro in her doctoral dissertation 3 showed that uniform nonsquareness is enough. In this work she also showed that WORTH plus 2-UNC implies the wFPP. In both of these cases the space X turns out to be reflexive. In 1994 Sims 4 himself proved that WORTH plus 0-inquadrate in every direction for some e0 2 implies the wFPP and in 2003 Dalby 5 showed that if X has WORTH and