Abstract
Let π be a unital Banach algebra and β³ be a unital π-bimodule. We show that if Ξ΄ is a linear mapping from π into β³ satisfying Ξ΄(ST)β=βΞ΄(S)Tβ+SΞ΄(T) for any S, Tβββπ with STβ=βW, where W is a left or right separating point of β³, then Ξ΄ is a Jordan derivation. Also, it is shown that every linear mapping h from π into a unital Banach algebra β¬ which satisfies h(S)h(T)β=βh(ST) for any S,βTβββπ with STβ=βW is a Jordan homomorphism if h(W) is a separating point of β¬.
Acknowledgement
This article is supported by the National Science Foundation of China.