LAUSR

UDC 517.98 Essential 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 Frechet algebras. Moreover, related results about Segal–Frechet algebras are provided. As the main result, it is provedthat if $(\mathcal{A} , p_{\ell})$ is an amenable Frechet algebra with a uniformly bounded approximate identity, then every symmetric Segal – Frechet algebra in $(\mathcal{A} , p_{\ell})$ is essentially amenable.