Fell-Bündel und verallgemeinerte L1-algebren - Leinert, Michael (Journal of functional analysis, 2004)
The relation between cross-sectional algebras of homogeneous Banach-∗-algebraic bundles in the sense of Fell [5] and generalized L1-algebras, as defined in slightly different ways by Leptin [7], Busby and Smith [2], and others, has been studied by Busby in [3]. We give an extension of his result, using a different method for obtaining topological group extensions. Instead of first constructing the abstract group extension from the given factor system and then topologizing it, we work in a natural topological setting and define a topological group which turns out to be the group extension belonging to the given factor system. As a consequence we obtain (without separability assumptions) that for any measurable factor system of a locally compact group with values in some other locally compact group the corresponding abstract group extension can be topologized to give a topological (and hence locally compact) group extension.