Abstract: Suppose that
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
is a real or complex unital Banach *-algebra,
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image002.png)
is a unital Banach
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
-bimodule, and G ∈
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
is a left separating point of
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image002.png)
. In this paper, we investigate whether the additive mapping
δ:
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
→
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image002.png)
satisfies the condition
A,B ∈
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
,
AB = G ⇒
Aδ(
B)+
δ(
A)
B*=
δ(G) characterize Jordan
*-derivations. Initially, we prove that if
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
is a real unital
C*-algebra and
G =
I is the unit element in
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
, then
δ (non-necessarily continuous) is a Jordan
*-derivation. In addition, we prove that if
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
is a real unital
C*-algebra and
δ is continuous, then
δ is a Jordan
*-derivation. Finally, we show that if
![](http://article.sciencepublishinggroup.com/journal/141/1411245/image001.png)
is a complex factor von Neumann algebra and
δ is linear, then
δ (non-necessarily continuous) is equal to zero.