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FRAMES IN HILBERT C*-MODULES AND MORITA EQUIVALENT C*-ALGEBRAS

  • MASSOUD AMINI (a1) (a2), MOHAMMAD B. ASADI (a3) (a4), GEORGE A. ELLIOTT (a5) and FATEMEH KHOSRAVI (a6)

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.

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FRAMES IN HILBERT C*-MODULES AND MORITA EQUIVALENT C*-ALGEBRAS

  • MASSOUD AMINI (a1) (a2), MOHAMMAD B. ASADI (a3) (a4), GEORGE A. ELLIOTT (a5) and FATEMEH KHOSRAVI (a6)

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