Local Lie $n$-Derivations of Reflexive Algebras

Abstract:

      Let $\mathcal{L}$ be a subspace lattice on a Banach space $X$ such that $X_{-} \neq X$ and $(0)_{+} \neq(0)$. We prove that every local Lie $n$-derivation from $\operatorname{Alg}\mathcal{L}$ into $B(X)$ is a Lie $n$-derivation.