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)

 

 

Commutator ideals and semicommutator ideals
of Toeplitz operators associated with flows II


Authors: Paul S. Muhly and Jingbo Xia
Journal: Proc. Amer. Math. Soc. 125 (1997), 3313-3319
MSC (1991): Primary 47B35, 47B47, 47C15.
MathSciNet review: 1402876
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for a flow with at most one fixed point, the commutator ideal and the semicommutator ideal of the associated Toeplitz algebra coincide. We further show that the situation becomes much more complicated for flows with at least two fixed points.


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

  • 1. W. Arveson, On groups of automorphisms of operator algebras, J. Funct. Anal. 15 (1974), 217-243.
  • 2. R. Curto, P. Muhly and J. Xia, Toeplitz operators on flows, J. Funct. Anal. 93 (1990), 391-450.
  • 3. R. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972.
  • 4. R. Douglas, Another look at real-valued index theory, (J. B. Conway and B. B. Morel eds.), Pitman Research Notes Math. Ser., Vol. 192, Longman Sci. Tch., 1988, pp. 91-120.
  • 5. F. Forelli, Analytic and quasi-invariant measures, Acta Math. 118 (1967), 33-59.
  • 6. I. Gohberg and N. Krupnik, The algebra generated by Toeplitz matrices, Funct. Anal. Appl. 3 (1969), 119-127.
  • 7. R. Loebl and P. Muhly, Analyticity and flows on von-Neumann algebras, J. Funct. Anal. 29 (1978), 214-252.
  • 8. P. Muhly, I. Putnam and J. Xia, On the $K$-theory of some $C^{\ast }$-algebras of Toeplitz and singular integral operators, J. Funct. Anal. 110 (1992), 161-225.
  • 9. P. Muhly and J. Xia, Commutator ideals and semicommutator ideals of Toeplitz algebras associated with flows, Proc. Amer. Math. Soc. 116 (1992), 1059-1066.
  • 10. G. Pederson, $C^{\ast }$-algebras and their automorphism groups, Academic Press, New York, 1979.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B35, 47B47, 47C15.

Retrieve articles in all journals with MSC (1991): 47B35, 47B47, 47C15.


Additional Information

Paul S. Muhly
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email: muhly@math.uiowa.edu

Jingbo Xia
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214
Email: JXMTH@ubvms.cc.buffalo.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03972-5
Received by editor(s): June 12, 1996
Additional Notes: This research was supported in part by grants from the National Science Foundation.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society