@article {
author = {Hosseini, Amin},
title = {A new proof of Singer-Wermer Theorem with some results on {g, h}-derivations.},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {11},
number = {1},
pages = {453-471},
year = {2020},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2019.17189.1915},
abstract = {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.},
keywords = {Derivation,Jordan derivation,Singer-Wermer Theorem,{g, h}-derivation,{g, h}-homomorphism},
url = {https://ijnaa.semnan.ac.ir/article_4360.html},
eprint = {https://ijnaa.semnan.ac.ir/article_4360_915f33e55799163f07a79115c6b19708.pdf}
}