Derivations of Fréchet Nuclear Gb∗-Algebras

It is an open question whether every derivation of a Fréchet GB∗-algebra A[Τ] is continuous. We give an affirmative answer for the case where A[Τ] is a smooth Fréchet nuclear GB∗-algebra. Motivated by this result, we give examples of smooth Fréchet nuclear GB∗-algebras which are not pro-C∗-algebras. © 2015 Australian Mathematical Publishing Association Inc.