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 | References | Similar Articles | Additional Information

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

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