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Paul S. Muhly and Baruch Solel
Morita transforms of tensor algebras view print
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| Published: |
January 30, 2011
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| Keywords: |
Morita equivalence, C*-correspondence, stabilization, representations, tensor algebra, Hardy algebra. |
| Subject: |
Primary: 46H25, 47L30, 47L55, Secondary: 46H25, 47L65 |
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Abstract
We show that if M and N are C*-algebras and if E (resp.
F) is a C*-correspondence over M (resp. N), then a
Morita equivalence between (E,M) and (F,N) implements an isometric
functor between the categories of Hilbert modules over the tensor
algebras of T+(E) and T+(F). We show
that this functor maps absolutely continuous Hilbert modules to absolutely
continuous Hilbert modules and provides a new interpretation of Popescu's
reconstruction operator.
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| Acknowledgements
The first author gratefully acknowledges research support from the U.S.-Israel Binational Science Foundation.
The second author gratefully acknowledges research support from the U.S.-Israel Binational Science Foundation and from the Lowengart Research Fund.
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| Author information
Paul S. Muhly:
Department of Mathematics, University of Iowa, Iowa City, IA 52242
paul-muhly@uiowa.edu
Baruch Solel:
Department of Mathematics, Technion, 32000 Haifa, Israel
mabaruch@techunix.technion.ac.il
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