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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compact operators on Hilbert modules


Authors: M. Anoussis and I. G. Todorov
Journal: Proc. Amer. Math. Soc. 133 (2005), 257-261
MSC (2000): Primary 46L05, 46H25; Secondary 47B07
Published electronically: June 23, 2004
MathSciNet review: 2086218
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Abstract: We prove that an adjointable contraction acting on a countably generated Hilbert module over a separable unital C*-algebra is compact if and only if the set of its second contractive perturbations is separable.


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Additional Information

M. Anoussis
Affiliation: Department of Mathematics, University of the Aegean, 832 00 Karlovassi, Samos, Greece
Email: mano@aegean.gr

I. G. Todorov
Affiliation: Department of Mathematics, University of the Aegean, 832 00 Karlovassi, Samos, Greece
Address at time of publication: Department of Pure Mathematics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland
Email: ivan@aegean.gr, i.todorov@qub.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07591-4
PII: S 0002-9939(04)07591-4
Keywords: Contractive perturbations, compact operators, Hilbert modules
Received by editor(s): February 6, 2002
Received by editor(s) in revised form: March 14, 2003, and October 13, 2003
Published electronically: June 23, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society