 

Paul S. Muhly and Baruch Solel
Morita transforms of tensor algebras view print


Published: 
January 30, 2011

Keywords: 
Morita equivalence, C*correspondence, stabilization, representations, tensor algebra, Hardy algebra. 
Subject: 
Primary: 46H25, 47L30, 47L55, Secondary: 46H25, 47L65 


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.


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.


Author information
Paul S. Muhly:
Department of Mathematics, University of Iowa, Iowa City, IA 52242
paulmuhly@uiowa.edu
Baruch Solel:
Department of Mathematics, Technion, 32000 Haifa, Israel
mabaruch@techunix.technion.ac.il

