Year: 2010
Author: Xiaofei Qi, Jinchuan Hou
Communications in Mathematical Research , Vol. 26 (2010), Iss. 2 : pp. 131–143
Abstract
Let $\mathcal{N}$ be a nest on a Banach space $X$, and Alg$\mathcal{N}$ be the associated nest algebra. It is shown that if there exists a non-trivial element in $\mathcal{N}$ which is complemented in $X$, then $D = (L_n)_{n∈N}$ is a Lie higher derivation of Alg$\mathcal{N}$ if and only if each $L_n$ has the form $L_n(A) = τ_n(A) + h_n(A)I$ for all $A ∈ {\rm Alg}\mathcal{N}$, where $(τ_n)_{n∈N}$ is a higher derivation and $(h_n)_{n∈N}$ is a sequence of additive functionals satisfying $h_n([A, B]) = 0$ for all $A, B ∈ {\rm Alg}\mathcal{N}$ and all $n ∈ \boldsymbol{N}$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-CMR-19167
Communications in Mathematical Research , Vol. 26 (2010), Iss. 2 : pp. 131–143
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: nest algebra higher derivation Lie higher derivation.