论文标题
与本地行动的Banach代数上（约旦）派生的特征
Characterizations of (Jordan) derivation on Banach algebra with local actions
论文作者
论文摘要
令$ \ mathcal {a} $为Unital Banach $*$ - 代数，而$ \ Mathcal {M} $为Unital $*$ - $ \ MATHCAL {A} $ -BIMODULE。如果$ w $是$ \ MATHCAL {M} $的左分离点，我们表明，每一个$*$ - 以$ W $为$ W $的可衍生映射是Jordan派生，而每个$*$ - 在$ W $中的每个$*$ - 在$ w $中都是Jordan左衍生绘制，是一个条件$ W \ Mathcal {a} a} = a} = $ natercal = w \ nativation。此外，我们从$ \ Mathcal {a} $从$ \ Mathcal {m} $中提供了线性映射$δ$和$τ$的完整描述b^*+a \circτ（b）^*= 0 $对于任何$ a，b \ in \ mathcal {a} $带有$ a \ circ b^*= 0 $，其中$ a \ circ b = ab+ba $是约旦产品。
Let $\mathcal{A}$ be a unital Banach $*$-algebra and $\mathcal{M}$ be a unital $*$-$\mathcal{A}$-bimodule. If $W$ is a left separating point of $\mathcal{M}$, we show that every $*$-derivable mapping at $W$ is a Jordan derivation, and every $*$-left derivable mapping at $W$ is a Jordan left derivation under the condition $W \mathcal{A}=\mathcal{A}W$. Moreover we give a complete description of linear mappings $δ$ and $τ$ from $\mathcal{A}$ into $\mathcal{M}$ satisfying $δ(A)B^*+Aτ(B)^*=0$ for any $A, B\in \mathcal{A}$ with $AB^*=0$ or $δ(A)\circ B^*+A\circτ(B)^*=0$ for any $A, B\in \mathcal{A}$ with $A\circ B^*=0$, where $A\circ B=AB+BA$ is the Jordan product.
