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Lie-type higher derivations on operator algebras. (English) Zbl 1341.47041

Summary: Motivated by the intensive and powerful works concerning additive mappings of operator algebras, we mainly study Lie-type higher derivations on operator algebras in the current work. It is shown that every Lie (triple-)higher derivation on some classical operator algebras is of standard form. The definition of Lie \(n\)-higher derivations on operator algebras and related potential research topics are properly-posed at the end of this article.

MSC:

47B47 Commutators, derivations, elementary operators, etc.
47C05 Linear operators in algebras
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