In this paper, we answer a question on derivations of dense algebras of linear operators posed by Brear and emrl. Our theorem implies the following result: let be a complex Banach algebra, and let d and g be continuous derivations of . If dg(x) is quasi-nilpotent for every x ∈ , then dg(x)3 lies in the radical of for every x ∈ . This result was proved by Brear and emrl with the additional assumption gd = dg.
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