Automatic Continuity of Surjective Almost Derivations on Frechet Q-Algebras

In ۱۹۷۱ R. L. Carpenter proved that every derivation T on a semisimple commutative Frechet algebra A with identity is continuous. By relaxing the commutativity assumption on A and adding the surjectivity assumption on T, we derive a corresponding continuity result, for a new concept of almost derivations on Frechet algebras in this article. Also, it is further proved that every surjective almost derivation T on non commutative semisimple Frechet Q-algebras A with an additional condition on A, is continuous. Moreover, an example is provided to illustrate our main result.

Keywords:

Almost derivation , Automatic continuity , Frechet Q-algebras.