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)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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

  • 1. B.E. Blackadar, A simple unital projectionless C*-algebra, J. Operator Theory 5 (1981), 63-71. MR 82h:46076
  • 2. J. Cuntz and G.K. Pedersen, Equivalence and traces on C*-algebras, J. Funct. Anal. 33 (1979), 135-164. MR 80m:46053
  • 3. G.A. Elliott and D. Evans, The structure of the irrational rotation C*-algebra, Ann. Math. 138 (1993), 477-501. MR 94j:46066
  • 4. R. Engelking, Dimension Theory, North-Holland, Amsterdam, Oxford and New York, 1978. MR 58:2753b
  • 5. T. Fack, Finite sums of commutators in C*-algebras, Ann. Inst. Fourier, Grenoble 32 (1982), 129-137. MR 83g:46051
  • 6. P.G. Ghatage and W.J. Phillips, C*-algebras generated by weighted shifts II, Indiana Univ. Math. J. 30 (1981), 539-545. MR 83h:46072
  • 7. I.N. Herstein, On the Lie and Jordan rings of a simple associative ring, Amer. J. Math. 77 (1955), 279-285.
  • 8. I.N. Herstein, Topics in Ring Theory, Chicago Lecture Notes in Mathematics, University of Chicago Press, Chicago and London, 1969. MR 42:6018
  • 9. L. Marcoux, On the closed Lie ideals of certain C*-algebras, J. Integr. Equat. Oper. Th. 22 (1995), 463-475. MR 96f:46123
  • 10. G.J. Murphy, C*-Algebras and Operator Theory, Academic Press, San Diego, 1990. MR 91m:46084
  • 11. G.K. Pedersen, The linear span of projections in simple C*-algebras, J. of Operator Theory 9 (1980), 289-296. MR 82b:46078
  • 12. K. Thomsen, Finite sums and products of commutators in inductive limit C*-algebras, Ann. Inst. Fourier, Grenoble 43 (1993), 225-249. MR 94g:46062

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L05

Retrieve articles in all journals with MSC (1991): 46L05

Additional Information

L. W. Marcoux
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

G. J. Murphy
Affiliation: Department of Mathematics, University College, Cork, Ireland

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

American Mathematical Society