Amenability modulo an ideal of Frechet algebras

TL;DR

This paper extends the concept of amenability modulo an ideal from Banach algebras to Frechet algebras, establishing foundational properties and characterizations.

Contribution

It introduces the notion of amenability modulo an ideal for Frechet algebras and links it to limits of Banach algebra amenability.

Findings

A Frechet algebra is amenable modulo an ideal iff it is a reduced limit of amenable Banach algebras.

The paper generalizes known Banach algebra results to Frechet algebras.

Provides new insights into the structure of amenable Frechet algebras.

Abstract

Amenability modulo an ideal of a Banach algebra have been defined and studied. In this paper we introduce the concept of amenability modulo an ideal of a Frechet algebra and investigate some known results about amenability modulo an ideal of a Frechet algebra. Also we show that a Frechet algebra A is amenable modulo an ideal if and only if A is isomorphic to a reduced limit of amenable modulo an ideal of Banach algebras.