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,pℯ) is an amenable Fréchet algebra with a uniformly bounded approximate identity, then every symmetric Segal–Fréchet algebra in (𝒜,pℯ) is essentially amenable.

中文翻译：

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Fréchet代数的基本适用性

Banach代数的基本适应性的概念已经定义和研究。我们为Fr'echet代数介绍这个概念。然后，将有关Banach代数的基本适应性的众多众所周知的结果推广到Fréchet代数。此外，还提供了Segal-Fréchet代数的相关结果。作为主要的结果，可以证明，如果（𝒜 ，P ℯ）是一种适合Fréchet可代数与一致有界近似身份，那么在（𝒜每对称西格尔-Fréchet可代数，P ℯ）基本上适合。