Lie Higher Derivations on Nest Algebras (Communications in Mathematical Research, 2021)
Let $\mathcal{N}$ be a nest on a Banach space $X$, and Alg$\mathcal{N}$ be the associatednest algebra. It is shown that if there exists a non-trivial element in $\mathcal{N}$ which iscomplemented in $X$, then $D = (L_n)_{n∈N}$ is a Lie higher derivation of Alg$\mathcal{N}$ if andonly 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 functionalssatisfying $h_n([A, B]) = 0$ for all $A, B ∈ {\rm Alg}\mathcal{N}$ and all $n ∈ \boldsymbol{N}$.