International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 28, Pages 1803-1806
doi:10.1155/S0161171203209108
Derivations on Banach algebras
S. Hejazian1
and S. Talebi2
1Department of Mathematics, Ferdowsi University, Mashhad, Iran
2Department of Mathematics, Payame Noor University, Mashhad, Iran
Abstract
Let D be a derivation on a Banach algebra; by using the operator D2, we give necessary and sufficient conditions for the separating ideal of D to be nilpotent. We also introduce an ideal M(D) and apply it to find out more equivalent conditions for the continuity of D and for nilpotency of its separating ideal.