## Taiwanese Journal of Mathematics

### JORDAN HIGHER ALL-DERIVABLE POINTS IN NEST ALGEBRAS

#### Abstract

Let $\mathcal{N}$ 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 $Alg\mathcal{N}$ into itself. We say that $d = \{d_n: n \in N\}$ is a Jordan higher derivable mapping at a given point $G$ if $d_{n}(ST+TS) = \sum\limits_{i+j=n} \{d_{i}(S) d_{j}(T) + d_{j}(T) d_{i}(S)\}$ for any $S,T \in Alg \mathcal{N}$ with $ST = G$. An element $G \in Alg \mathcal{N}$ 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 $Alg\mathcal{N}$ is a Jordan higher all-derivable point. This extends some results in [1] to the case of higher derivations.

#### Article information

Source
Taiwanese J. Math., Volume 16, Number 6 (2012), 1959-1970.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406833

Digital Object Identifier
doi:10.11650/twjm/1500406833

Mathematical Reviews number (MathSciNet)
MR3001829

Zentralblatt MATH identifier
1272.47090

#### Citation

Zhen, Nannan; Zhu, Jun. JORDAN HIGHER ALL-DERIVABLE POINTS IN NEST ALGEBRAS. Taiwanese J. Math. 16 (2012), no. 6, 1959--1970. doi:10.11650/twjm/1500406833. https://projecteuclid.org/euclid.twjm/1500406833

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