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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A generalized dual for a $C^*$-algebra
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by Herbert Halpern PDF
Trans. Amer. Math. Soc. 153 (1971), 139-156 Request permission

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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Additional Information
  • © Copyright 1971 American Mathematical Society
  • 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