Banach代数上双导子的Hyers-Ulam-Rassias稳定性

On the Hyers-Ulam-Rassias stability of biderivations on Banach algebras

设A是Banach代数,M是Banach A模.从A到M的双导子是指二元线性映射B:A2→M且满足x,y,u,v∈A都有B(xy,u)=xB(y,u)+B(x,u)y和B(x,uv)=B(x,u)v+uB(x,v).采用直接构造的方法证明了从A到M上的双导子是Hyers-Ulam-Rassias稳定的.

Let A be a Banach algebra, and M be a Banach A-bimodule. A bilinear mapping B：A2→M is called abiderivationfromA into Mif B（xy,u）=xB（y,u）＋B（x,u）y and B（x,uv）=B（x,u）v uB（x,v） for all x,y,u,v∈A. In this paper,we prove the Hyers-Ulam-Rassias stability of biderivations from A into M using the direct method.