@Article{CMR-26-2,
author = {Xiaofei, Qi and Jinchuan, Hou},
title = {Lie Higher Derivations on Nest Algebras},
journal = {Communications in Mathematical Research },
year = {2010},
volume = {26},
number = {2},
pages = {131--143},
abstract = {<p style="text-align: justify;">Let&nbsp;$\mathcal{N}$&nbsp;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 $n ∈&nbsp;\boldsymbol{N}$.</p>},
issn = {2707-8523},
doi = {https://doi.org/2010-CMR-19167},
url = {https://global-sci.com/article/81901/lie-higher-derivations-on-nest-algebras}
}