A universal topological transformation group inL 2 (G × G)

Abstract

LetG denote an infinite,σ-compact, locally compact topological group. In this paper a construction is given for a topological transformation groupHG with the Hilbert spaceL 2 (G × G) as a phase space such that any topological transformation group (G, X, π) can be embedded inH G , providedX is a separable metrizable space andπ is a bounded action. The class of such topological transformation groups contains all actions ofG on separable, metrizable, locally compact spaces.