Let A A be a C β C^* -algebra acting on a Hilbert space H H , let Ο : A β B ( H ) Ο :Aβ B(H) be a linear mapping and let d : A β B ( H ) d:Aβ B(H) be a Ο Ο -derivation. Generalizing the celebrated theorem of Sakai, we prove that if Ο Ο is a continuous β * -mapping, then d d is automatically continuous. In addition, we show the converse is true in the sense that if d d is a continuous β * - Ο Ο -derivation, then there exists a continuous linear mapping Ξ£ : A β <
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Mirzavaziri et al. (2006) studied this question.