Let $\mathfrak{A}$ be an algebra. A linear mapping $\delta:\mathfrak{A}\to\mathfrak{A}$ is called a \textit{derivation} if $\delta(ab)=\delta(a)b+a\delta(b)$ for each $a,b\in\mathfrak{A}$. Given two derivations $\delta$ and $\delta'$ on a $C^*$-algebra $\mathfrak A$, we prove that there exists a derivation $\Delta$ on $\mathfrak A$ such that $\delta\delta'=\Delta^2$ if and only if either $\delta'=0$ or $\delta=s\delta'$ for some $s\in\mathbb{C}$.
Ekrami, K., Mirzavaziri, M. & Ebrahimi Vishki, H. R. (2016). Product of derivations on C$^*$-algebras. International Journal of Nonlinear Analysis and Applications, 7(2), 109–114. https://doi.org/10.22075/ijnaa.2017.451
MLA
Ekrami, K., Mirzavaziri, M., & Ebrahimi Vishki, H. R. "Product of derivations on C$^*$-algebras", International Journal of Nonlinear Analysis and Applications, 7, 2, 2016, 109–114. doi: 10.22075/ijnaa.2017.451
HARVARD
Ekrami, K., Mirzavaziri, M., & Ebrahimi Vishki, H. R. (2016). 'Product of derivations on C$^*$-algebras', International Journal of Nonlinear Analysis and Applications, 7(2), pp. 109–114. doi: 10.22075/ijnaa.2017.451
CHICAGO
Ekrami, K., Mirzavaziri, M. & Ebrahimi Vishki, H. R., "Product of derivations on C$^*$-algebras." International Journal of Nonlinear Analysis and Applications, 7 2 (2016): 109–114, doi: 10.22075/ijnaa.2017.451
VANCOUVER
Ekrami K., Mirzavaziri M., Ebrahimi Vishki H. R. Product of derivations on C$^*$-algebras. IJNAA. 2016;7(2):109–114. doi: 10.22075/ijnaa.2017.451
International Journal of Nonlinear Analysis and Applications