Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-04-07591-4
Published electronically: June 23, 2004
MathSciNet review: 2086218
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • 1. 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. M. Anoussis and E. G. Katsoulis, Compact operators and the geometric structure of C*-algebras, Proc. Amer. Math. Soc. 124 (1996), no. 7, 2115 - 2122.MR 96i:46068
  • 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
  • 5. R. L. Moore and T. T. Trent, Extreme points of certain operator algebras, Indiana Univ. Math. J. 36 (1987), 645-650. MR 89d:47103
  • 6. G. Pedersen, C*-algebras and their automorphism groups, Academic Press, London 1979. MR 81e:46037

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L05, 46H25, 47B07

Retrieve articles in all journals with MSC (2000): 46L05, 46H25, 47B07


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: https://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

American Mathematical Society