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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 28, Pages 1803-1806

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 Hindawi Publishing Corporation. 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.


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.