The equation ${dd'+d'd=D^2}$ for derivations on C$^*$-algebras

Authors : Sayed Khalil Ekrami, Madjid Mirzavaziri

Pages : 21-27

View : 11 | Download : 7

Publication Date : 9999-12-31

Article Type : Makaleler

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.
Keywords : Derivation, C$^*$-algebra