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Lie triple derivations on nest algebras. (English) Zbl 1124.47054
Summary: Let $\delta$ be a Lie triple derivation from a nest algebra ${\cal A}$ into an ${\cal A}$-bimodule ${\cal M}$. We show that if ${\cal M}$ is a weak* closed operator algebra containing ${\cal A}$, then there are an element $S\in{\cal M}$ and a linear functional $f$ on ${\cal A}$ such that $\delta(A) = SA - AS + f (A)I$ for all $A\in{\cal A}$, and if ${\cal M}$ is the ideal of all compact operators, then there is a compact operator $K$ such that $\delta(A) = KA - AK$ for all $A\in{\cal A}$. As applications, Lie derivations and Jordan derivations on nest algebras are characterized.

47L35Nest algebras, CSL algebras
17B60Lie (super)algebras associated with other structures
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