@article{1186.47036,
author="Mirzavaziri, M. and Naranjani, K. and Niknam, A.",
title="{Innerness of higher derivations.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="4",
number="2",
pages="121-128",
year="2010",
abstract="{Summary: Let $\mathcal{A}$ be an algebra. A sequence $\{d_n\}$ of
    linear mappings on $\mathcal{A}$ is called a higher derivation if $d_n(ab) =
    \sum_{k=0}^n d_k(a)d_{n-k}(b)$ for each $a, b \in \mathcal{A}$ and each
    nonnegative integer $n$. In this paper, a notion of an inner higher
    derivation is given. We characterize all uniformly bounded inner higher
    derivations on Banach algebras and show that each uniformly bounded higher
    derivation on a Banach algebra $\mathcal{A}$ is inner provided that each
    derivation on $\mathcal{A}$ is inner.}",
keywords="{derivation; inner derivation; $(\sigma;\sigma)$-derivation; inner
    $(\sigma;\sigma)$- derivation; higher derivation; inner higher derivation;
    generating function}",
classmath="{*47B47 (Derivations and linear operators defined by algebraic
    conditions)
16W25 (Derivations, actions of Lie algebras (assoc. rings and algebras))
}",
}