## Lie ideals in triangular operator algebras

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- by T. D. Hudson, L. W. Marcoux and A. R. Sourour PDF
- Trans. Amer. Math. Soc.
**350**(1998), 3321-3339 Request permission

## 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 $\mathcal {K} \subseteq \mathcal {L} \subseteq \mathcal {K}+ \mathfrak {D}_{\mathcal {K}}$.## References

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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)
- © Copyright 1998 American Mathematical Society
- 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