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

 

Unitarily-invariant linear spaces in C*-algebras


Authors: L. W. Marcoux and G. J. Murphy
Journal: Proc. Amer. Math. Soc. 126 (1998), 3597-3605
MSC (1991): Primary 46L05
MathSciNet review: 1610753
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Abstract: Characterisations and containment results are given for linear subspaces of a unital C*-algebra that are invariant under conjugation by sets of unitary elements of the algebra. The (unitarily-invariant) linear span of the projections in a simple, unital C*-algebra having non-scalar projections is shown to contain all additive commutators of the algebra and, in certain cases, to be equal to the algebra.


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Additional Information

L. W. Marcoux
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: l.marcoux@ualberta.ca

G. J. Murphy
Affiliation: Department of Mathematics, University College, Cork, Ireland
Email: gjm@ucc.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04934-X
PII: S 0002-9939(98)04934-X
Keywords: Unitarily-invariant spaces, simple C*-algebras
Received by editor(s): April 16, 1997
Received by editor(s) in revised form: April 21, 1997
Additional Notes: The first author’s research was supported in part by NSERC (Canada).
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society