product of derivations on c$^*$-algebras

Authors

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 hamid reza ebrahimi vishki

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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Journal title:
international journal of nonlinear analysis and applications

جلد ۷، شماره ۲، صفحات ۱۰۹-۱۱۴

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