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New York Journal of Mathematics
Volume 29 (2023), 29-50

  

G. K. Eleftherakis and E. Papapetros

Hilbert modules, rigged modules, and stable isomorphism

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Published: December 17, 2022.
Keywords: Operator algebras, C*-algebras, Hilbert modules, TRO, stable isomorphism, Morita equivalence.
Subject [2010]: 47L30 (primary), 46L05, 46L08, 47L05, 47L25, 16D90 (secondary).

Abstract
Rigged modules over an operator algebra are a generalization of Hilbert modules over a C*-algebra. We characterize the rigged modules over an operator algebra A which are orthogonally complemented in C(A), the space of infinite columns with entries in A. We show that every such rigged module 'restricts' to a bimodule of Morita equivalence between appropriate stably isomorphic operator algebras.

Acknowledgements

N/A


Author information

G. K. Eleftherakis:
University of Patras
Faculty of Sciences, Department of Mathematics
265 00 Patras, Greece

gelefth@math.upatras.gr

E. Papapetros:
University of Patras
Faculty of Sciences, Department of Mathematics
265 00 Patras, Greece

e.papapetros@upatras.gr