TY - JOUR
ID - 3098
TI - Local higher derivations on C*-algebras are higher derivations
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Naranjani, Lila
AU - Hassani, Mahmoud
AU - Mirzavaziri, Madjid
AD - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad
91775, Iran
Y1 - 2018
PY - 2018
VL - 9
IS - 1
SP - 111
EP - 115
KW - Higher derivation
KW - local higher derivation
KW - Derivation
KW - local derivation
DO - 10.22075/ijnaa.2018.3098
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_3098.html
L1 - https://ijnaa.semnan.ac.ir/article_3098_2dd5a1ec2b9eb291b3144ecc1e96595e.pdf
ER -