We prove that every continuous conjugate linear mapping from a unital C $$^*$$ -algebra A into its dual space, $$A^*$$ , which is ternary derivable at the unit element of A is a ternary derivation. This is somehow a ternary-counterpart result for (binary) derivations on associative algebras which proves that any linear continuous map from a unital C $$^*$$ -algebra A into a Banach A-bimodule which is derivable at the unit element of A, is a derivation.

中文翻译：

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将来自 C$$^*$$-代数的线性映射共轭到它们的对偶空间中，这些对偶空间在单位元素上是三元可推导的

我们证明了从单位 C $$^*$$ -代数 A 到它的对偶空间 $$A^*$$ 的每个连续共轭线性映射，$$A^*$$ 在 A 的单位元素上是三元可导的。这在某种程度上是关联代数的（二元）推导的三元对应结果，它证明了从单位 C $$^*$$ -代数 A 到 Banach A-双模的任何线性连续映射，其可在单位元素A，是推导。