Renorming of and the fixed point property |
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Authors: | Pei-Kee Lin |
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Affiliation: | aDepartment of Mathematics, University of Memphis, TN 38152, United States |
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Abstract: | For any , let Pk denote the natural projections on ℓ1. Let |||||| be an equivalent norm of ℓ1 that satisfies all of the following four conditions:- (1) There are α>4 and a positive (decreasing) sequence (αn) in (0,1) such that for any normalized block basis {fn} of (ℓ1,||||||) and xℓ1 with Pk−1(x)=x and |||x|||<αk,
- (2) There are two strictly decreasing sequences {βk} and {γk} with such that for any normalized block basis {fn} of (ℓ1,||||||) and x with (I−Pk)(x)=x,
- (3) For any , I−Pk=1.
- (4) The unit ball of (ℓ1,||||||) is σ(ℓ1,c0)-closed.
In this article, we prove that the space (ℓ1,||||||) has the fixed point property for the nonexpansive mapping. This improves a previous result of the author. Keywords: Renorming; Fixed point property |
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Keywords: | Renorming Fixed point property |
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