Bulletin of the
Korean Mathematical Society BKMS

The main goal of this paper is to show the following: Let $d$ and $g$ be (continuous or discontinuous) linear derivations on a Banach algebra $A$ over a complex field $\Bbb C$ such that $\alpha d^{3}+dg$ is a linear Jordan derivation for some $\alpha \in \Bbb C$. Then the product $dg$ maps $A$ into the Jacobson radical of $A$.

Keywords: Banach algebra, derivation, Jacobson radical

MSC numbers: Primary 47B47; Secondary 46H40