J. Li

[ 1 ] - Left derivable or Jordan left derivable mappings on Banach algebras

Let $\mathcal{A}$ be a unital Banach algebra, $\mathcal{M}$ be a left $\mathcal{A}$-module, and $W$ in $\mathcal{Z}(\mathcal{A})$ be a left separating point of $\mathcal{M}$. We show that if $\mathcal{M}$ is a unital left $\mathcal{A}$-module and $\delta$ is a linear mapping from $\mathcal{A}$ into $\mathcal{M}$, then the following four conditions are equivalent: (i) $\delta$ is a Jordan left der…