A renorming in some Banach spaces with applications to fixed point theory
| Autor: | Maria A. Japón, Carlos A. Hernandez Linares |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Discrete mathematics
Renorming theory Mathematics::Functional Analysis Fourier–Stieltjes algebra Topology of convergence locally in measure Banach space Fixed-point theorem Nonexpansive mappings Fixed point Separable space Combinatorics Compact group Norm (mathematics) Bounded function Fixed point theory Fourier algebras Subspace topology Analysis Mathematics |
| Zdroj: | Journal of Functional Analysis. 258(10):3452-3468 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2009.10.025 |
| Popis: | We consider a Banach space X endowed with a linear topology τ and a family of seminorms { R k ( ⋅ ) } which satisfy some special conditions. We define an equivalent norm ⦀ ⋅ ⦀ on X such that if C is a convex bounded closed subset of ( X , ⦀ ⋅ ⦀ ) which is τ-relatively sequentially compact, then every nonexpansive mapping T : C → C has a fixed point. As a consequence, we prove that, if G is a separable compact group, its Fourier–Stieltjes algebra B ( G ) can be renormed to satisfy the FPP. In case that G = T , we recover P.K. Lin's renorming in the sequence space l 1 . Moreover, we give new norms in l 1 with the FPP, we find new classes of nonreflexive Banach spaces with the FPP and we give a sufficient condition so that a nonreflexive subspace of L 1 ( μ ) can be renormed to have the FPP. |
| Databáze: | OpenAIRE |
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