# Locally bounded approximate diagonal modulo an ideal of Frechet algebras

## TL;DR

This paper extends the concept of bounded approximate diagonals modulo an ideal from Banach algebras to Frechet algebras, exploring their relation to amenability.

## Contribution

It introduces the notion of locally bounded approximate diagonals modulo an ideal for Frechet algebras and studies their connection to amenability.

## Key findings

- Defined locally bounded approximate diagonals modulo an ideal for Frechet algebras
- Established the relationship between amenability modulo an ideal and these diagonals
- Extended previous Banach algebra results to the Frechet algebra setting

## Abstract

For a Banach algebra A and a closed ideal I, the notion of bounded approximate diagonal modulo I has been studied and investigated. In this paper we define the notion of locally bounded approximate diagonal modulo an ideal I for a Frechet algebra A and obtain the relation between amenability modulo an ideal I and the existence of locally bounded approximate diagonals modulo I.