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

Published online by Cambridge University Press:  03 August 2016

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: [email protected]
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: [email protected]
GEORGE A. ELLIOTT
Affiliation:
Department of Mathematics, University of Toronto, Toronto M5S 2E4, Canada e-mail: [email protected]
FATEMEH KHOSRAVI
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

REFERENCES

1. Bakic, D. and Guljas, B., Hilbert C*-modules over C*-algebras of compact operators, Acta. Sci. Math. 68 (2002), 249269.Google Scholar
2. Dixmier, J., Les C*-algèbres et leurs représentations (Gauthier-Villars, Paris, 1964).Google Scholar
3. Duffin, R. and Schaeffer, A., A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341366.Google Scholar
4. Frank, M. and Larson, D. R., Frames in Hilbert C*-modules and C*-algebras, J. Operator Theory 48 (2000), 273314.Google Scholar
5. Kasparov, G., Hilbert C*-modules: Theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), 133150.Google Scholar
6. Lance, C., Hilbert C*-modules, London Math. Soc. Lecture Note Series, 210 (Cambridge University Press, Cambridge, 1995).Google Scholar
7. Li, H., A Hilbert C*-module admitting no frames, Bull. London Math. Soc. 42 (2010), 388394.CrossRefGoogle Scholar
8. Manuilov, V. and Troitsky, E., Hilbert C*-modules, Translations of Mathematical Monographs, vol. 226 (American Mathematical Society, Providence, 2005).Google Scholar
9. Murphy, G. J., C*-algebras and operator theory (Academic Press, New York, 1990).Google Scholar
10. Raeburn, L. and Williams, D. P., Morita equivalence and continuous-trace C*-algebras, Mathematical Surveys and Monographs, vol. 60 (American Mathematical Society, Providence, 1998).Google Scholar
11. Rieffel, M. A., Morita equivalence for C*-algebras and W*-algebras, J. Pure Appl. Algebra 5 (1974), 5194.Google Scholar