AUTOMATIC CONTINUITY OF SURJECTIVE ALMOST DERIVATIONS ON FRECHET Q-ALGEBRAS

In 1971 R. L. Carpenter proved that every derivation T on a semisimple commutative Frechet algebra ʌ with identity is continuous. By relaxing the commutativity assumption on ʌ 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 ʌ with an additional condition on ʌ, is continuous. Moreover, an example is provided to illustrate our main result.