Product of derivations on C$^*$-algebras

Authors

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

Khalil Ekrami Department of Mathematics, Payame Noor University

Madjid Mirzavaziri 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 $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. 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 $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdelta'$ for some $sinmathbb{C}$.

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