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Transactions of the American Mathematical Society

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The properties $ \sp{\ast} $-regularity and uniqueness of $ C\sp{\ast} $-norm in a general $ \sp{\ast} $-algebra


Author: Bruce A. Barnes
Journal: Trans. Amer. Math. Soc. 279 (1983), 841-859
MSC: Primary 46K05; Secondary 46K10
DOI: https://doi.org/10.1090/S0002-9947-1983-0709587-7
MathSciNet review: 709587
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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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DOI: https://doi.org/10.1090/S0002-9947-1983-0709587-7
Article copyright: © Copyright 1983 American Mathematical Society

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