On the Lie ideals of C*-algebras

2015/05/18 by Robert, Leonel · 1 voice · 1 citation
#16W10 #46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1505.04503

Abstract

Various questions on Lie ideals of C*-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.

Cited by

• Commutators of finite multiplicative order

Discussions

• There is no such example. Indeed, Theorem . Let $A$ be a $C^*$ algebra. If $a \in A$ is such that $a^k = 0$ , where $k \geq 2$ , then $a$ is a sum of $k-1$ commutators in $A$ . Proof. We may assume th [stackexchange, 0 points]

Related

• Lie ideals in properly infinite C*-algebras
• Prime and semiprime Lie ideals in C*-algebras
• C-Ideals of Lie Algebras
• Prime ideals in C*-algebras and applications to Lie theory
• Lie Ideals in Operator Algebras