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
DOI:
https://doi.org/10.1090/S0002-9947-98-02117-5
MathSciNet review:
1458325
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Abstract | References | Similar Articles | Additional Information
Abstract: We study Lie ideals in two classes of triangular operator algebras: nest algebras and triangular UHF algebras. Our main results show that if $\mathcal {L}$ is a closed Lie ideal of the triangular operator algebra $\mathbb {A}$, then there exist a closed associative ideal $\mathcal {K}$ and a closed subalgebra $\mathfrak {D}_{\mathcal {K}}$ of the diagonal $\mathbb {A}\cap \mathbb {A}^*$ so that $\mathcal {K} \subseteq \mathcal {L} \subseteq \mathcal {K}+ \mathfrak {D}_{\mathcal {K}}$.
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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
MR Author ID:
288388
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
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