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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 | ||
| تاریخ دریافت: 11 خرداد 1400، تاریخ بازنگری: 10 فروردین 1401، تاریخ پذیرش: 19 فروردین 1401 | ||
| 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 | ||
| مراجع | ||
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