The properties *-regularity and uniqueness of ๐ถ*-norm in a general *-algebra
Bruce Alan Barnes ยท Transactions of the American Mathematical Society ยท 1983
In this paper two properties of a โ ^{\ast } -algebra A A are considered which are concerned with the relationship between the algebra and its C โ {C^{\ast }} -enveloping algebra. These properties are that A A have a unique C โ {C^{\ast }} -norm, and that A A be โ ^{\ast } -regular. Both of these concepts are closely involved with the representation theory of the algebra.