Jordan Higher All-Derivable Points in Nest Algebras

Nannan Zhen; Jun Zhu

paper

Jordan Higher All-Derivable Points in Nest Algebras

arXiv:1112.5590

Abstract

Let $N$ be a non-trivial and complete nest on a Hilbert space $H$ . Suppose $d = {d_{n} : n \in N}$ is a group of linear mappings from Alg $N$ into itself. We say that $d = {d_{n} : n \in N}$ is a Jordan higher derivable mapping at a given point $G$ if $d_{n} (S T + S T) = i + j = n \sum {d_{i} (S) d_{j} (T) + d_{j} (T) d_{i} (S)}$ for any $S, T \in A l g N$ with $S T = G$ . An element $G \in A l g N$ is called a Jordan higher all-derivable point if every Jordan higher derivable mapping at $G$ is a higher derivation. In this paper, we mainly prove that any given point $G$ of Alg $N$ is a Jordan higher all-derivable point. This extends some results in \cite{Chen11} to the case of higher derivations.

15