Essential amenability of Fréchet algebras

UDC 517.98Essential amenability of Banach algebras have been defined and investigated. Here, this concept will be introduced for Frechet algebras. Then a number of well-known results of essential amenability of Banach algebras are generalized for Fréchet algebras. Moreover, related results about Segal–Fréchet algebras are provided. As the main result, it is provedthat if ( , p ℓ ) is an amenable Fréchet algebra with a uniformly bounded approximate identity, then every symmetric Segal – Fréchet algebra in ( , p ℓ ) is essentially amenable.