Essential Amenability of Fréchet Algebras

Abstract

The notion of essential amenability of Banach algebras has been defined and investigated. We introduce this concept for Fr´echet algebras. Then numerous well-known results concerning the essential amenability of Banach algebras are generalized for Fréchet algebras. Moreover, related results for the Segal–Fréchet algebras are also provided. As the main result, it is proved that if (A,pl) is an amenable Fréchet algebra with a uniformly bounded approximate identity, then every symmetric Segal–Fréchet algebra in (A,pl) is essentially amenable. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.