The Fixed Point Property in c0 with an Equivalent Norm

Berta Gamboa de Buen and Fernando Núñez-Medina

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: We study the fixed point property (FPP) in the Banach space c0 with the equivalent norm ∥·∥D. The space c0 with this norm has the weak fixed point property. We prove that every infinite‐dimensional subspace of (c0, ∥·∥D) contains a complemented asymptotically isometric copy of c0, and thus does not have the FPP, but there exist nonempty closed convex and bounded subsets of (c0, ∥·∥D) which are not ω‐compact and do not contain asymptotically isometric c0—summing basis sequences. Then we define a family of sequences which are asymptotically isometric to different bases equivalent to the summing basis in the space (c0, ∥·∥D), and we give some of its properties. We also prove that the dual space of (c0, ∥·∥D) over the reals is the Bynum space l1∞ and that every infinite‐dimensional subspace of l1∞ does not have the fixed point property.

Date: 2011
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https://doi.org/10.1155/2011/574614

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:574614

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