Lie Higher Derivations on Nest Algebras

Lie Higher Derivations on Nest Algebras

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 $n ∈ \boldsymbol{N}$.

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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.

Author Details

Xiaofei Qi

Jinchuan Hou