Frames in Hilbert C∗-modules and Morita equivalent C∗-algebras

Abstract

We show that the property of a C∗-algebra that all its Hilbert modules have a frame, in the case of σ-unital C∗-algebras, is preserved under Rieffel-Morita equivalence. In particular, we show that a σ-unital continuous-trace C∗-algebra with trivial Dixmier-Douady class, all of whose Hilbert modules admit a frame, has discrete spectrum. We also show this for the tensor product of any commutative C∗-algebra with the C∗-algebra of compact operators on any Hilbert space. © Glasgow Mathematical Journal Trust 2016.