Stable normed algebras

TL;DR

This paper introduces the concept of stability in normed algebras, exploring its fundamental properties and characterizations, with implications for the theory of almost multiplier maps.

Contribution

It defines a new stability property for normed algebras and characterizes stable algebras among similar classes, advancing the theoretical understanding.

Findings

Stability is a key property in normed algebras.

Stable algebras are characterized within similar algebra classes.

The concept impacts the study of almost multiplier maps.

Abstract

In this paper we introduce a new property for normed algebras. This property which we call it stability, plays a key role in the studying of the theory of almost multiplier maps. In this note we study some of the basic properties of this notion and characterize stable algebras among similar algebras.