Turkish Journal of Mathematics
Abstract
Let $\mathcal{A}$ be an algebra. A linear mapping $d:\mathcal{A}\to\mathcal{A}$ is called a derivation if $d(ab)=d(a)b+ad(b)$ for each $a,b\in\mathcal{A}$. Given two derivations $d$ and $d'$ on a C$^*$-algebra $\mathcal{A}$, we prove that there exists a derivation $D$ on $\mathcal A$ such that $dd'+d'd=D^2$ if and only if $d$ and $ d' $ are linearly dependent.
DOI
10.3906/mat-1601-88
Keywords
Derivation; C$^*$-algebra
First Page
21
Last Page
27
Recommended Citation
EKRAMI, SAYED KHALIL and MIRZAVAZIRI, MADJID
(2018)
"The equation ${dd'+d'd=D^2}$ for derivations on C$^*$-algebras,"
Turkish Journal of Mathematics: Vol. 42:
No.
1, Article 3.
https://doi.org/10.3906/mat-1601-88
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss1/3
