Document Type : Research Paper

Authors

• Khalil Ekrami ¹
• Madjid Mirzavaziri ²
• Hamid Reza Ebrahimi Vishki ³

¹ Department of Mathematics, Payame Noor University

² Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad

³ Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Struc-tures (CEAAS), Ferdowsi University of Mashhad,

Abstract

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 ${\delta }^{\prime }$ on a $C^{\ast }$-algebra $\mathfrak{A}$, we prove that there exists a derivation $\mathrm{\Delta }$ on $\mathfrak{A}$ such that $\delta {\delta }^{\prime }={\mathrm{\Delta }}^2$ if and only if either ${\delta }^{\prime }=0$ or $\delta =s{\delta }^{\prime }$ for some $s\in \mathbb{C}$.

Keywords

• Derivation
• C${}^{\ast }$-algebra