%0 Journal Article
%T Local higher derivations on C*-algebras are higher derivations
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Naranjani, Lila
%A Hassani, Mahmoud
%A Mirzavaziri, Madjid
%D 2018
%\ 08/01/2018
%V 9
%N 1
%P 111-115
%! Local higher derivations on C*-algebras are higher derivations
%K Higher derivation
%K local higher derivation
%K Derivation
%K local derivation
%R 10.22075/ijnaa.2018.3098
%X Let $\mathfrak{A}$ be a Banach algebra. We say that a sequence $\{D_n\}_{n=0}^\infty$ of continuous operators form $\mathfrak{A}$ into $\mathfrak{A}$ is a \textit{local higher derivation} if to each $a\in\mathfrak{A}$ there corresponds a continuous higher derivation $\{d_{a,n}\}_{n=0}^\infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $\mathfrak{A}$ is a $C^*$-algebra then each local higher derivation on $\mathfrak{A}$ is a higher derivation. We also prove that each local higher derivation on a $C^*$-algebra is automatically continuous.
%U https://ijnaa.semnan.ac.ir/article_3098_2dd5a1ec2b9eb291b3144ecc1e96595e.pdf