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.
Naranjani, L., Hassani, M., Mirzavaziri, M. (2018). Local higher derivations on C*-algebras are higher derivations. International Journal of Nonlinear Analysis and Applications, 9(1), 111-115. doi: 10.22075/ijnaa.2018.3098
MLA
Lila Naranjani; Mahmoud Hassani; Madjid Mirzavaziri. "Local higher derivations on C*-algebras are higher derivations". International Journal of Nonlinear Analysis and Applications, 9, 1, 2018, 111-115. doi: 10.22075/ijnaa.2018.3098
HARVARD
Naranjani, L., Hassani, M., Mirzavaziri, M. (2018). 'Local higher derivations on C*-algebras are higher derivations', International Journal of Nonlinear Analysis and Applications, 9(1), pp. 111-115. doi: 10.22075/ijnaa.2018.3098
VANCOUVER
Naranjani, L., Hassani, M., Mirzavaziri, M. Local higher derivations on C*-algebras are higher derivations. International Journal of Nonlinear Analysis and Applications, 2018; 9(1): 111-115. doi: 10.22075/ijnaa.2018.3098
)