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.

DOI:
https://doi.org/10.1090/S0002-9939-97-03972-5

MathSciNet review:
1402876

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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.

**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 -theory of some -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,*-algebras and their automorphism groups*, Academic Press, New York, 1979.

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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