Speaker
Description
Let $\mathcal{M}$ be a $\ast$-algebra with unity $I$ and a non-trivial projection $P$. For any $D, E \in \mathcal{M}$, the operations $
D \diamond E = DE + ED \quad \text{and} \quad D \bullet E = DE + ED^\ast
$ are known respectively as the Jordan product and the Jordan $*$-product. If a map $\Omega: \mathcal{M} \to \mathcal{M}$ such that
\begin{eqnarray}
\Omega(D_1 \diamond D_2 \diamond \cdots \bullet D_n) = \sum_{k=1}^{n} D_1 \diamond \cdots \diamond D_{k-1} \diamond \Omega(D_k) \diamond D_{k+1} \diamond \cdots \bullet D_n
\end{eqnarray} for all $ D_1, D_2, \ldots, D_n \in \mathcal{M}$, then $\Omega$ is an additive $\ast$-derivation. As an applications, we can also expand our result on prime $\ast$-algebras, factor von-Neumann algebra of type $I_1$, factor von-Neumann algebra and standard operator algebra.
