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Compact operators on Hilbert modules
Author(s):
M.
Anoussis;
I.
G.
Todorov
Journal:
Proc. Amer. Math. Soc.
133
(2005),
257-261.
MSC (2000):
Primary 46L05, 46H25;
Secondary 47B07
Posted:
June 23, 2004
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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.
References:
-
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- C. Akemann and N. Weaver, Geometric characterizations of some classes of operators in C*-algebras and von Neumann algebras, Proc. Amer. Math. Soc. 130 (2002), 3033-3037.MR 2003e:46093
- 2.
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- 3.
- M. Anoussis and E. G. Katsoulis, Compact operators and the geometric structure of nest algebras, Indiana Univ. Math. J. 46 (1997), no.1, 319-335.MR 98e:47066b
- 4.
- G. G. Kasparov, Hilbert C*-modules, theorems of Stinespring and Voiculescu, J. Op. Theory 4 (1980), 133-150. MR 82b:46074
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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:
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
Posted:
June 23, 2004
Communicated by:
David R. Larson
Copyright of article:
Copyright
2004,
American Mathematical Society
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