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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Representations of locally convex $ \sp{\ast} $-algebras


Author: James D. Powell
Journal: Proc. Amer. Math. Soc. 44 (1974), 341-346
MSC: Primary 46K10
DOI: https://doi.org/10.1090/S0002-9939-1974-0361803-X
MathSciNet review: 0361803
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Abstract: Conditions for a functional to be admissible on a locally convex $ \ast $-algebra are defined. Let $ F$ be an admissible positive Hermitian functional on a commutative locally convex $ \ast $-algebra; then it is shown that there exists a representation of $ A$ into a Hilbert space. Sufficient conditions for a functional $ F$ to be representable are also given.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0361803-X
Keywords: Locally convex $ \ast $-algebras, representation theory, pseudocomplete locally convex $ \ast $-algebras, $ \ast $-representations, admissible functionals, representable functionals
Article copyright: © Copyright 1974 American Mathematical Society