Thickness in topological transformation semigroups (Q687855)

On a semigroup \(S\) the concept of left thickness was introduced by \textit{T. Mitchell} [Trans. Am. Math. Soc. 119, 244-261 (1965; Zbl 0146.120)] and generalized by \textit{H. D. Junghenn} [Proc. Am. Math. Soc. 75, 37-41 (1979; Zbl 0423.43002)]. Let \(F\) be a norm-closed algebra of bounded functions on \(S\), containing the constant functions, left-translation invariant and such that \(T_ \mu(f) \in F\) whenever \(f \in F\), \(\mu\in F^*\) with \(T_ \mu(f)(s) = \mu(T_ sf)\), \(T_ sf(t) = f(st)\), \(s,t \in S\). The author transposes this notion to continuous transformation groups and establishes a large collection of equivalent properties.