@article {
author = {Naranjani, Lila and Hassani, Mahmoud and Mirzavaziri, Madjid},
title = {Local higher derivations on C*-algebras are higher derivations},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {9},
number = {1},
pages = {111-115},
year = {2018},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2018.3098},
abstract = {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.},
keywords = {Higher derivation,local higher derivation,Derivation,local derivation},
url = {https://ijnaa.semnan.ac.ir/article_3098.html},
eprint = {https://ijnaa.semnan.ac.ir/article_3098_2dd5a1ec2b9eb291b3144ecc1e96595e.pdf}
}