Let $A$ be a (complex) Banach algebra. The object of this paper shall beremove the continuity of derivation in the recently theorems. We provethat every derivation $D$ on $A$ satisfying $[D(a), a] in ext{Prad}(A)$ for all $a in A$ maps into the radical of $A$. Also if $lphaD^3 + D^2$ is a derivation for some $lpha in C$ and all minimalprime ideals are closed, then $D$ maps into its radical.
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机译：令$ A $为（复杂的）Banach代数。本文的目的应是消除最近定理中的导数的连续性。我们证明$ A $上的每个派生$ D $满足$ [D（a），a] in {text {Prad}（A）$）中所有$ a in $的映射都映射到$ A $的根。同样，如果$ alphaD ^ 3 + D ^ 2 $是C $中某些$ alpha 的派生词，并且所有最小素理想都已封闭，则$ D $会映射到其激进形式。
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