The properties *-regularity and uniqueness of 𝐶*-norm in a general *-algebra

Abstract

In this paper two properties of a ∗ ^{\ast } -algebra A A are considered which are concerned with the relationship between the algebra and its C ∗ {C^{\ast }} -enveloping algebra. These properties are that A A have a unique C ∗ {C^{\ast }} -norm, and that A A be ∗ ^{\ast } -regular. Both of these concepts are closely involved with the representation theory of the algebra.