Asymptotically non-expansive actions of strongly amenable semigroups and fixed points (Q1706366)

Let \(S\) be a semi-topological semigroup and let \(LMC(S)\) be the space of left multiplicatively continuous functions on \(S\). The authors study conditions under which \(LMC(S)\) is strongly left amenable (in this case it is left amenable). One of the main results says that \(LMC(S)\) is strongly left amenable if and only if there exists a compact \(S\)-preserving group in \(\Delta (LMC(S))\). Here \(\Delta (LMC(S))\) is the spectrum of \(LMC(S)\) consisting of all multiplicative means on \(LMC(S)\) with the weak* topology.