an:05702418 Zbl 1186.47036 Mirzavaziri, M.; Naranjani, K.; Niknam, A. Innerness of higher derivations. EN Banach J. Math. Anal. 4, No. 2, 121-128, electronic only (2010). ISSN 1735-8787/e 2010

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*47B47 16W25 derivation; inner derivation; $(\sigma;\sigma)$-derivation; inner $(\sigma;\sigma)$- derivation; higher derivation; inner higher derivation; generating function 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.