Essential amenability of Fréchet algebras

  • F. Abtahi Dep. Pure Math., Univ. Isfahan, Iran
  • S. Rahnama Dep. Pure Math., Univ. Isfahan, Iran
Keywords: Fr´echet algebra, Banach algebra

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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Published
15.07.2020
How to Cite
Abtahi , F., and S. Rahnama. “Essential Amenability of Fréchet Algebras”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 7, July 2020, pp. 867-76, doi:10.37863/umzh.v72i7.830.
Section
Research articles