Abstract
Let [Formula: see text] be a unital prime ∗-algebra containing a nontrivial projection [Formula: see text]. In this paper, it is shown that if a mapping [Formula: see text] satisfies [Formula: see text] or [Formula: see text] for all [Formula: see text], where [Formula: see text] and [Formula: see text], then [Formula: see text] preserves self-adjoint elements. Therefore, the two relations (0.1) and (0.2) will be equivalent for every [Formula: see text] and [Formula: see text]. This result makes possible to unify the conclusions in a single statement which implies the above two results. In fact, it is shown that if a map [Formula: see text] satisfies the conditions in (0.1) or (0.2) for every [Formula: see text] and [Formula: see text], then [Formula: see text] is an additive ∗-derivation.
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