Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Commutator ideals and semicommutator ideals of Toeplitz operators associated with flows II
HTML articles powered by AMS MathViewer

by Paul S. Muhly and Jingbo Xia PDF
Proc. Amer. Math. Soc. 125 (1997), 3313-3319 Request permission

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
  • W. Arveson, On groups of automorphisms of operator algebras, J. Funct. Anal. 15 (1974), 217-243.
  • R. Curto, P. Muhly and J. Xia, Toeplitz operators on flows, J. Funct. Anal. 93 (1990), 391-450.
  • R. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972.
  • 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.
  • F. Forelli, Analytic and quasi-invariant measures, Acta Math. 118 (1967), 33-59.
  • I. Gohberg and N. Krupnik, The algebra generated by Toeplitz matrices, Funct. Anal. Appl. 3 (1969), 119-127.
  • R. Loebl and P. Muhly, Analyticity and flows on von-Neumann algebras, J. Funct. Anal. 29 (1978), 214-252.
  • 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.
  • P. Muhly and J. Xia, Commutator ideals and semicommutator ideals of Toeplitz algebras associated with flows, Proc. Amer. Math. Soc. 116 (1992), 1059-1066.
  • 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
  • MR Author ID: 215486
  • Email: JXMTH@ubvms.cc.buffalo.edu
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3313-3319
  • MSC (1991): Primary 47B35, 47B47, 47C15
  • DOI: https://doi.org/10.1090/S0002-9939-97-03972-5
  • MathSciNet review: 1402876