$b$-Generalized derivations on Banach algebras
Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 57-64
https://doi.org/10.4134/CKMS.c200480
Published online July 20, 2021
Printed January 31, 2022
Husain Alhazmi
King Abdulaziz University
Abstract : In this paper, we show, among others, that if $A$ is a Banach algebra satisfying a functional identity involving a $b$-generalized derivation $F$ on $A$, under some mild conditions, is of the form $F(x)=ax$ for all $x\in R$, where $a\in Q_r$, a right Martindale quotient ring of $A$.
Keywords : Banach algebra, $b$-generalized derivation, right Martindale quotient ring
MSC numbers : 16W25, 46J10
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