an: Zbl 1186.47036
au: Mirzavaziri, M.; Naranjani, K.; Niknam, A.
ti: Innerness of higher derivations.
la: EN
so: Banach J. Math. Anal. 4, No. 2, 121-128, electronic only (2010).
py: 2010
dt: J
cc: *47B47 16W25
ut: derivation; inner derivation; $(\sigma;\sigma)$-derivation; inner
    $(\sigma;\sigma)$- derivation; higher derivation; inner higher derivation;
    generating function
ab: 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.