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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A generalized dual for a $ C\sp*$-algebra


Author: Herbert Halpern
Journal: Trans. Amer. Math. Soc. 153 (1971), 139-156
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9947-1971-0270165-X
MathSciNet review: 0270165
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Abstract: Let $ \mathcal{A}$ be a $ {C^ \ast }$-algebra, let $ \mathcal{B}$ be its enveloping von Neumann algebra, and let $ \mathcal{F}$ be the center of $ \mathcal{B} $. Let $ {\mathcal{B}_ \sim }$ be the set of all $ \sigma $-weakly continuous $ \mathcal{F}$-module homomorphisms of the $ \mathcal{F}$-module $ \mathcal{B}$ into $ \mathcal{F}$ and let $ {\mathcal{A}^ \sim }$ be the set of all restrictions to $ \mathcal{A}$ of elements of $ {\mathcal{B}_ \sim }$. Then $ \mathcal{A}$ is classified as CCR, GCR, and NGCR in terms of certain naturally occurring topologies on $ {\mathcal{A}^ \sim }$.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0270165-X
Keywords: $ {C^ \ast }$-algebra, von Neumann algebra, GCR and NGCR algebra, module homomorphism into the center
Article copyright: © Copyright 1971 American Mathematical Society

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