Extension properties of WS-groups (Q1188323)

Continuing earlier results [e.g. ibid. 41, No. 3, 357-372 (1990; Zbl 0701.43013); see also ibid. 46, 146-151 (1993; Zbl 0765.43005)] the authors study topological groups in which every weakly almost periodic function \(f\) is already ``strictly'' w.a.p., i.e. \(\{f_ g^ h\); \(g,h\in G\}\) is weakly relative compact; \(f_ g^ h(x)=f(hxg)\). They show that any such group \(G\) has a base of neighbourhoods invariant under inner automorphisms if the topology of \(G\) is induced by the w.a.p. functions (in particular if \(G\) is locally compact). Furthermore several conditions are given, which insure that certain extensions of such groups again have this property.