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

Barnes, Bruce A.

doi:10.1090/S0002-9947-1983-0709587-7

The properties $^{\ast }$-regularity and uniqueness of $C^{\ast }$-norm in a general $^{\ast }$-algebra
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Trans. Amer. Math. Soc. 279 (1983), 841-859 Request permission

Abstract:

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

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