Abstract: Suppose that
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is a real or complex unital Banach *-algebra,
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is a unital Banach
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-bimodule, and G ∈
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is a left separating point of
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. In this paper, we investigate whether the additive mapping
δ:
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→
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satisfies the condition
A,B ∈
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,
AB = G ⇒
Aδ(
B)+
δ(
A)
B*=
δ(G) characterize Jordan
*-derivations. Initially, we prove that if
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is a real unital
C*-algebra and
G =
I is the unit element in
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, then
δ (non-necessarily continuous) is a Jordan
*-derivation. In addition, we prove that if
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is a real unital
C*-algebra and
δ is continuous, then
δ is a Jordan
*-derivation. Finally, we show that if
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is a complex factor von Neumann algebra and
δ is linear, then
δ (non-necessarily continuous) is equal to zero.