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A new proof of Singer-Wermer Theorem with some results on {g, h}-derivations. | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 41، دوره 11، شماره 1، تیر 2020، صفحه 453-471 اصل مقاله (177.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.17189.1915 | ||
| نویسنده | ||
| Amin Hosseini* | ||
| Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran | ||
| تاریخ دریافت: 21 بهمن 1397، تاریخ بازنگری: 21 اسفند 1397، تاریخ پذیرش: 26 اسفند 1397 | ||
| چکیده | ||
| Singer and Wermer proved that if $\mathcal{A}$ is a commutative Banach algebra and $d: \mathcal{A}\longrightarrow \mathcal{A}$ is a continuous derivation, then $d(\mathcal{A}) ⊆ rad(\mathcal{A})$, where $rad(\mathcal{A})$ denotes the Jacobson radical of $\mathcal{A}$. In this paper, we establish a new proof of that theorem. Moreover, we prove that every continuous Jordan derivation on a finite dimensional Banach algebra, under certain conditions, is identically zero. As another objective of this article, we study {g, h}-derivations on algebras. In this regard, we prove that if f is a {g, h}-derivation on a unital algebra, then f, g and h are generalized derivations. Additionally, we achieve some results concerning the automatic continuity of {g, h}-derivations on Banach algebras. In the last section of the article, we introduce the concept of a {g, h}-homomorphism and then we present a characterization of it under certain conditions. | ||
| کلیدواژه‌ها | ||
| derivation؛ Jordan derivation؛ Singer-Wermer Theorem؛ {g, h}-derivation؛ {g, h}-homomorphism | ||
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