Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2022; 37(1): 57-64

Online first article July 20, 2021      Printed January 31, 2022

https://doi.org/10.4134/CKMS.c200480

Copyright © The Korean Mathematical Society.

$b$-Generalized derivations on Banach algebras

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 $xin R$, where $ain Q_r$, a right Martindale quotient ring of $A$.

Keywords: Banach algebra, $b$-generalized derivation, right Martindale quotient ring

MSC numbers: 16W25, 46J10