A note on power values of generalized derivation in prime ring and noncommutative Banach algebras
Subject Areas : History and biography
Sh. Sahebi
1
(Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO.
Code 14168-94351, Iran)
V. Rahmani
2
(Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO.
Code 14168-94351, Iran)
Keywords: prime ring, Banach algebras, generalized derivation, Martindale quotient ring,
Abstract :
Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivationof $R$ and $n\geq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,y\in R$; (2) obtain some related result in case $R$ is a noncommutativeBanach algebra and $H$ is continuous or spectrally bounded.