International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 28, Pages 1803-1806
doi:10.1155/S0161171203209108
Derivations on Banach algebras
1Department of Mathematics, Ferdowsi University, Mashhad, Iran
2Department of Mathematics, Payame Noor University, Mashhad, Iran
Received 12 September 2002
Copyright © 2003 S. Hejazian and S. Talebi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.