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Journal of Operator Theory

Volume 75, Issue 2, Spring 2016  pp. 387-408.

On the Lie ideals of $\Cstar$-algebras

Authors:  Leonel Robert
Author institution: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, 70506, U.S.A.

Summary: Various questions on Lie ideals of $\Cstar$-algebras are investigated. They fall roughly under the following topics: relation of Lie ideals to closed two-sided ideals; Lie ideals spanned by special classes of elements such as commutators, nilpotents, and the range of polynomials; characterization of Lie ideals as similarity invariant subspaces.

Keywords: Lie ideals, $\Cstar$-algebras, commutators, nilpotents, polynomials, similarity invariant subspaces

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