A Morita equivalence for Hilbert $C^*$-modules
Volume 209 / 2012
Studia Mathematica 209 (2012), 11-19
MSC: Primary 46L08; Secondary 46L05.
DOI: 10.4064/sm209-1-2
Abstract
We introduce a notion of Morita equivalence for Hilbert $C^*$-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert $C^*$-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert $C^*$-modules. We also present an extension of Green's theorem in the context of Hilbert $C^*$-modules.
