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:
https://doi.org/10.1090/S0002-9939-98-04934-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