Abstract
Let [Formula: see text] be a unital prime ∗-ring containing a nontrivial symmetric idempotent and let [Formula: see text] be the maximal symmetric ring of quotients of [Formula: see text]. Using the technique of Peirce decomposition and the theory of functional identities, we prove that a map [Formula: see text] satisfies [Formula: see text] for all [Formula: see text] if and only if [Formula: see text] is an additive ∗-derivation unless [Formula: see text] and [Formula: see text]. As an application, we shall characterize such maps in different operator algebras.
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