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Let Abe a semisimple H*-algebra and let T: AAbe an additive mapping such that T(x n +1)=T(x)x n+x n T(x) holds for all xAand some integer n≥1. In this case Tis a left and a right centralizer.

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Let Rbe a 2-torsion free semiprime *-ring and let T:R?Rbe an additive mapping such that T(xx*)=T(x)x* is fulfilled for all x ?R. In this case T(xy)=T(x)yholds for all pairs x,y?R.

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