Weak amenability of frechet algebras

Abstract

Let A be a Fréchet algebra. We introduce and study the notion of weak amenability of A. In fact we show that some results in the field of weak amenability of Banach algebras can be generalized for Fréchet algebras. For example we prove that if A is weakly amenable then A is essential. Moreover if I is a quasinormable closed ideal in the Fréchet algebra A such that A I and I are weakly amenable, then A is weakly amenable, as well.