Ideal and weak Amenability of Fréchet locally $C^{\ast }$-algebra

Abstract

The notion of Fréchet locally $C^{\ast }$-algebra generalizes the notion of $C^{\ast }$-algebra. In this paper, we first present some definitions and basic facts about locally $C^{\ast }$-algebra, and then we introduce and study the notion of ideal and weak amenability for these algebras. Also, we show that every Fréchet locally $C^{\ast }$-algebra is ideally amenable.

arXiv commentarXiv admin note: text overlap with arXiv:2111.13752