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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lie ideals in triangular operator algebras


Authors: T. D. Hudson, L. W. Marcoux and A. R. Sourour
Journal: Trans. Amer. Math. Soc. 350 (1998), 3321-3339
MSC (1991): Primary 47D25, 46K50
MathSciNet review: 1458325
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Abstract: We study Lie ideals in two classes of triangular operator algebras: nest algebras and triangular UHF algebras. Our main results show that if ${\mathfrak L}$ is a closed Lie ideal of the triangular operator algebra ${\mathcal A}$, then there exist a closed associative ideal ${\mathcal K}$ and a closed subalgebra ${\mathfrak D}_{\mathcal K}$ of the diagonal ${\mathcal A}\cap {\mathcal A}^*$ so that ${\mathcal K}\subseteq {\mathfrak L}\subseteq {\mathcal K}+ {\mathfrak D}_{\mathcal K}$.


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Additional Information

T. D. Hudson
Affiliation: Department of Mathematics\ East Carolina University\ Greenville, North Carolina, 27858-4353
Email: tdh@math.ecu.edu

L. W. Marcoux
Affiliation: Department of Mathematical Sciences\ University of Alberta\ Edmonton, Alberta, Canada T6G 2G1
Email: L.Marcoux@ualberta.ca

A. R. Sourour
Affiliation: Department of Mathematics\ University of Victoria\ Victoria, British Columbia, Canada V8W 3P4
Email: sourour@math.uvic.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02117-5
PII: S 0002-9947(98)02117-5
Received by editor(s): October 4, 1996
Additional Notes: This research was supported in part by an NSF grant (to Hudson) and by NSERC (of Canada) grants (to Marcoux and Sourour)
Article copyright: © Copyright 1998 American Mathematical Society