Bull. Korean Math. Soc. 2022; 59(2): 277-283
Online first article March 31, 2022 Printed March 31, 2022
https://doi.org/10.4134/BKMS.b200772
Copyright © The Korean Mathematical Society.
Jiankui Li, Shan Li, Kaijia Luo
East China University of Science and Technology; East China University of Science and Technology; East China University of Science and Technology
Let $\mathcal{A}$ be a unital Banach algebra, $\mathcal{M}$ a unital $\mathcal{A}$-bimodule, and $\delta$ a linear mapping from $\mathcal{A}$ into $\mathcal{M}$. We prove that if $\delta$ satisfies $\delta(A)A^{-1}+A^{-1}\delta(A)+A\delta(A^{-1})+\delta(A^{-1})A=0$ for every invertible element $A$ in $\mathcal{A}$, then $\delta$ is a Jordan derivation. Moreover, we show that $\delta$ is a Jordan derivable mapping at the unit element if and only if $\delta$ is a Jordan derivation. As an application, we answer the question posed in [4, Problem 2.6].
Keywords: Derivation, Jordan derivation, Triple derivation
MSC numbers: Primary 47B47, 47L35, 47B49
Supported by: This research was partly supported by the National Natural Science Foundation of China (Grant No.11871021).
2021; 58(5): 1193-1208
1999; 36(3): 477-481
2001; 38(4): 709-718
2002; 39(2): 211-224
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd