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

Part of: Selfadjoint operator algebras Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  03 August 2016

MASSOUD AMINI ,
MOHAMMAD B. ASADI ,
GEORGE A. ELLIOTT  and
FATEMEH KHOSRAVI
MASSOUD AMINI
Affiliation:
School of Mathematics, Tarbiat Modares University, Tehran 14115 134, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746, Iran e-mail: mamini@modares.ac.ir
MOHAMMAD B. ASADI
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5746, Iran e-mail: mb.asadi@khayam.ut.ac.ir
GEORGE A. ELLIOTT
Affiliation:
Department of Mathematics, University of Toronto, Toronto M5S 2E4, Canada e-mail: elliott@math.toronto.edu
FATEMEH KHOSRAVI
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran e-mail: fa.khosravi@stu-mail.um.ac.ir
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Abstract

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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.

MSC classification

Primary: 46L08: $C^*$-modules
Secondary: 42C15: General harmonic expansions, frames 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 1 , January 2017 , pp. 1 - 10
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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