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Linearizability of Non-expansive Semigroup Actions on Metric Spaces

Lutz Schröder
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Abstract

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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Lutz Schröder. 2006-12-21. Linearizability of Non-expansive Semigroup Actions on Metric Spaces. https://doi.org/10.1016/j.topol.2007.04.022

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