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 Results on the range of derivations Bull. Korean Math. Soc. 2000 Vol. 37, No. 2, 265-272 Yong-Soo Jung Chungnam National University Abstract : Let $D$ be a derivation on a Banach algebra $A$. Suppose that $[[D(x),x],D(x)]$ lies in the nil radical of $A$ for all $x \in A$. Then $D(A)$ is contained in the Jacobson radical of $A$. Keywords : derivation, prime algebra, Banach algebra, nil radical, Jacobson radical MSC numbers : 46H05, 47B47 Downloads: Full-text PDF