Title of article :
A new proof of Singer-Wermer Theorem with some results on {g, h}-derivations
Author/Authors :
Hosseini, Amin Department of Mathematics - Kashmar Higher Education Institute, Kashmar, Iran
Pages :
19
From page :
453
To page :
471
Abstract :
Singer and Wermer proved that if A is a commutative Banach algebra and d: A → A is a continuous derivation, then d(A) ⊆ rad(A), where rad(A) denotes the Jacobson radical of 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
Journal title :
International Journal of Nonlinear Analysis and Applications
Serial Year :
2020
Record number :
2606162
Link To Document :
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