Segal Frechet algebras

TL;DR

This paper introduces Segal Frechet algebras, explores their properties, and characterizes their closed ideals, extending the theory of abstract Segal algebras to the Frechet algebra setting.

Contribution

It defines Segal Frechet algebras, investigates their properties, and characterizes their closed ideals, advancing the understanding of topological algebra structures.

Findings

Established the concept of Segal Frechet algebras.

Proved the ideal theorem for Frechet algebras.

Characterized closed ideals of Segal Frechet algebras.

Abstract

Let (A,p_l)_{l\in\Bbb N} be a Frechet algebra. In this paper, we introduce the concept of Segal Frechet algebra and investigate known results about abstract Segal algebras, for Segal Frechet algebras. Also we recall the concept of approximate identities for topological algebras and provide some remarkable results for Segal Frechet algebras. Moreover, we verify ideal theorem for Frechet algebras and characterize closed ideals of Segal Frechet algebra (B,q_m)_{m\in\Bbb N} in (A,p_l)_{l\in\Bbb N}.