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