C*-Segal algebras with order unit
Jukka Kauppi, Martin Mathieu

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.
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