Jordan higher all-derivable points in triangular algebras

Jun Zhu; Jinping Zhao

paper

Jordan higher all-derivable points in triangular algebras

arXiv:1107.3190

Abstract

Let $T$ be a triangular algebra. We say that $D = {D_{n} : n \in N} \subseteq L (T)$ is a Jordan higher derivable mapping at $G$ if $D_{n} (S T + T S) = \sum_{i + j = n} (D_{i} (S) D_{j} (T) + D_{i} (T) D_{j} (S))$ for any $S, T \in T$ with $S T = G$ . An element $G \in T$ is called a Jordan higher all-derivable point of $T$ if every Jordan higher derivable linear mapping $D = {D_{n}}_{n \in N}$ at $G$ is a higher derivation. In this paper, under some mild conditions on $T$ , we prove that some elements of $T$ are Jordan higher all-derivable points. This extends some results in [6] to the case of Jordan higher derivations.

15 pages