
Summary: In this note, we give a description of Jordan \(*\)-derivations on standard operator algebras with respect to the Jordan product defined by \(A\circ B =\frac 12 (AB +BA)\). That is, we characterize the additive solutions of the functional equation \(E(T \circ T) = T \circ E(T) + E(T) \circ T^*\) (\(T \in A\)), where \(\mathcal A\subset \mathcal B(H)\) is a standard operator algebra.
Matrix and operator functional equations, Jordan product, Jordan \(*\)-derivation, Commutators, derivations, elementary operators, etc.
Matrix and operator functional equations, Jordan product, Jordan \(*\)-derivation, Commutators, derivations, elementary operators, etc.
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