TY - JOUR
ID - 4360
TI - A new proof of Singer-Wermer Theorem with some results on {g, h}-derivations.
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Hosseini, Amin
AD - Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
Y1 - 2020
PY - 2020
VL - 11
IS - 1
SP - 453
EP - 471
KW - Derivation
KW - Jordan derivation
KW - Singer-Wermer Theorem
KW - {g, h}-derivation
KW - {g, h}-homomorphism
DO - 10.22075/ijnaa.2019.17189.1915
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_4360.html
L1 - https://ijnaa.semnan.ac.ir/article_4360_915f33e55799163f07a79115c6b19708.pdf
ER -