Linearizability of Non-expansive Semigroup Actions on Metric Spaces

Lutz Schröder

In: Topology and its Applications, Vol. 155, Pages 1576-1579, 2008.


We show that a non-expansive action of a topological semigroup S on a metric space X is linearizable iff its orbits are bounded. The crucial point here is to prove that X can be extended by adding a fixed point of S, thus allowing application of a semigroup version of the Arens-Eells linearization, iff the orbits of S in X are bounded.

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