Linearizability of Non-expansive Semigroup Actions on Metric Spaces
arXiv:math/0612553 · doi:10.1016/j.topol.2007.04.022
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.