%0 Journal Article
%T A new proof of Singer-Wermer Theorem with some results on {g, h}-derivations.
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Hosseini, Amin
%D 2020
%\ 04/01/2020
%V 11
%N 1
%P 453-471
%! A new proof of Singer-Wermer Theorem with some results on {g, h}-derivations.
%K Derivation
%K Jordan derivation
%K Singer-Wermer Theorem
%K {g, h}-derivation
%K {g, h}-homomorphism
%R 10.22075/ijnaa.2019.17189.1915
%X 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.
%U https://ijnaa.semnan.ac.ir/article_4360_915f33e55799163f07a79115c6b19708.pdf