C*-Segal algebras with order unit

TL;DR

This paper introduces noncommutative C*-Segal algebras as dense ideals in C*-algebras, explores their properties, and characterizes those with an order unit using multiplier module theory.

Contribution

It defines C*-Segal algebras, investigates their fundamental properties, and provides a structure theorem for those with an order unit.

Findings

C*-Segal algebras are dense ideals in C*-algebras.

The structure of C*-Segal algebras with order units is characterized.

Multiplier modules are used to analyze these algebras.

Abstract

We introduce the notion of a (noncommutative) C*-Segal algebra as a Banach algebra which is a dense ideal in a C*-algebra. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of C*-Segal algebras with order unit is determined.