The fixed point property for a class of nonexpansive maps in L\sp\infty(Ω,Σ,μ)

Details The fixed point property for a class of nonexpansive maps in L\sp\infty(Ω,Σ,μ) The fixed point property for a class of nonexpansive maps in L\sp\infty(Ω,Σ,μ)

2004-04-12

arxiv.org/abs/math/0404235v1

Mathematics

Functional Analysis

4 pages

Scientific paper

For a finite and positive measure space $(\Omega,\Sigma,\mu)$ and any weakly
compact convex subset of $L\sp\infty(\Omega,\Sigma,mu)$, a fixed point theorem
for a class of nonexpansive self-mappings is proved. An analogous result is
obtained for the space $C(\Omega)$. An illustrative example is given.

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