Integration as a generalization of the integral operator

	Integration as a generalization of the integral operator
International Journal of Nonlinear Analysis and Applications
مقاله 21، دوره 14، شماره 6، شهریور 2023، صفحه 273-280 اصل مقاله (382.32 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.23562.2558
نویسندگان
Nosrat Baloochshahriyari¹؛ Alireza Janfada^* ¹؛ Madjid Mirzavaziri^* ²
¹Department of Mathematics, University of Birjand, Birjand, Iran
²Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad
چکیده
Let $\mathfrak{A}$ be an algebra. A \textit{derivation} on $\mathfrak{A}$ is a linear mapping $\delta:\mathfrak{A}\to\mathfrak{A}$ such that $\delta(ab)=\delta(a)b+a\delta(b)$ for every $a,b\in\mathfrak{A}$. As a dual to this notion, we consider a linear mapping $\Delta:\mathfrak{A}\to\mathfrak{A}$ with the property $\Delta(a)\Delta(b)=\Delta(\Delta(a)b+a\Delta(b))$ for every $a,b\in\mathfrak{A}$ and we call it an \textit{integration}. In this paper, we give some examples, counterexamples and facts concerning integrations on algebras. Furthermore, we state and prove a characterization for integrations on finite dimensional matrix algebras.
کلیدواژه‌ها
Derivation؛ integration؛ C*-algebra؛ matrix algebra
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