On the stability of bi-derivations in Banach algebras
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 959-967
https://doi.org/10.4134/BKMS.2011.48.5.959
Printed September 1, 2011
Yong-Soo Jung and Kyoo-Hong Park
Sun Moon University, Seowon University
Abstract : Let $\mathcal A$ be a Banach algebra and let $f:\mathcal A\times\mathcal A\to\mathcal A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, $\mathcal A$ is unital, then $f:\mathcal A\times\mathcal A\to\mathcal A$ is an exact bi-derivation. Moreover, if $\mathcal A$ is unital, prime and $f$ is symmetric, then $f=0$.
Keywords : bi-derivation, approximate bi-derivation, stability
MSC numbers : 39B72, 39B52
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