- The image of a continuous strong higher derivation is contained in the radical
- Jun, Kil-Woung ; Lee, Young-Whan ;
- Bulletin of the Korean Mathematical Society, volume 33, issue 2, 1996, Pages 229~232
Abstract
Let A be a Banach algebra over the complex field. A linear map $D : A \to A$ is a derivation if D(xy) = xD(y) + D(x)y for all $x,y \ in A$. A sequence ${H_0, H_1, \cdots, H_m}$ (resp. ${H_0, H_1, \cdots}$) of linear operators on A is a higher derivation of rank m (resp. infinitely rank) if for each n = 0, 1, 2, $\cdots$, m (resp. n = 0, 1, 2, \cdots$) and any x, y $\in$ A, $$ H_n(xy) = \sum_{i=0}^{n} H_i (x) H_{n-i} (y). $$