Linear derivations in Banach algebras
Bull. Korean Math. Soc. 2001 Vol. 38, No. 3, 443-447
Yong-Soo Jung
Chungnam National University
Abstract : 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
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