$n$-ideal and $n$-weak amenability of Frechet algebras

TL;DR

This paper introduces and explores the concepts of $n$-ideal and $n$-weak amenability in Frechet algebras, extending existing notions from Banach algebras and analyzing their properties and relationships.

Contribution

It generalizes the notions of $n$-ideal and $n$-weak amenability from Banach to Frechet algebras and investigates their properties and interrelations.

Findings

Established definitions of $n$-ideal and $n$-weak amenability for Frechet algebras.

Analyzed inherited properties and relations between different types of amenability.

Explored the connection between these amenability concepts and the unitization of Frechet algebras.

Abstract

In this paper, we introduce and study some notations of amenability such as $n$-ideal amenability and $n$-weak amenability for Frechet algebra and we examine how these concepts in Banach algebra can be generalized and defined for Frechet algebra. We will also examine some inherited properties of $n$-ideal and $n$-weak amenable Frechet algebra and determine the relations between $m$ and $n$-weak amenability and $m$ and $n$-ideal amenability for Frechet algebra. Also, the relation of these new concepts of amenability of a Frechet algebra and its unitization is investigated.