Direct sums of renormings of ℓ1 and the fixed point property


Let γn be an increasing sequence in (0,1) that converges to 1, and let ∥·∥ be the equivalent norm of ℓ1 defined by ∥(ak)=sup γn n∈ℕγn∑ k=n∞|ak|. In this article, we show that for any m>1, the space (∑i=1m⊕(ℓ1, ∥·∥))1 is not isometrically isomorphic to any subspace of (ℓ1,∥·∥) and it has the fixed point property. © 2010 Elsevier Ltd. All rights reserved.

Publication Title

Nonlinear Analysis, Theory, Methods and Applications