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Fixed point set of semigroups of non-expansive mappings and amenability. (English) Zbl 1142.47035
The author studies the fixed point set of a strongly continuous nonexpansive semigroup $\{T(t)\}_{t\in S}$ acting in a Banach space. He investigates the cases when $S$ is a semi-topological semigroup for which $CB(S)$ (the space of bounded continuous functions) is $n$-extremely amenable, and when $S$ is an additive sub-semigroup of a locally convex vector space. Some applications to harmonic analysis are also provided.

MSC:
47H20Semigroups of nonlinear operators
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
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References:
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