We prove a general version
of Mackey’s Imprimitivity Theorem for induced representations of locally compact
groups. Let G be a locally compact group and let H be a closed subgroup. Following
Rieffel we show, using Morita equivalence of Banach algebras, that systems of
imprimitivity for induction from strongly continuous Banach H−modules to strongly
continuous Banach G−modules can be described in terms of an action on the induced
module of C0(G∕H), the algebra of complex continuous functions on G∕H
vanishing at ∞, which is compatible with the G−homogeneous structure of
G∕H and the strong operator topology continuity of the module action of
G.
