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Lie ideals in triangular operator algebras

Authors:	T D Hudson L W Marcoux A R Sourour

Institution:	Department of Mathematics, East Carolina University, Greenville, North Carolina 27858-4353 ; Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 ; Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4

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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