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Proceedings of the American Mathematical Society

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

 

 

Duality in $ B\sp{\ast} $-algebras


Author: Sheila A. McKilligan
Journal: Proc. Amer. Math. Soc. 38 (1973), 86-88
MSC: Primary 46J10; Secondary 46K05
DOI: https://doi.org/10.1090/S0002-9939-1973-0326396-0
MathSciNet review: 0326396
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Abstract: Let $ X$ be a locally compact Hausdorff space and let $ {C_0}(X)$ be the algebra of continuous functions on $ X$ vanishing at infinity. Then $ {C_0}(X)$ is a dual algebra if and only if the operator $ \mu \to fd\mu $ is weakly completely continuous on $ {C_0}{(X)^ \ast }$ for all $ f \in {C_0}(X)$. This improves a recent result of P. K. Wong and provides a description of dual $ {B^ \ast }$-algebras.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0326396-0
Keywords: Dual $ {B^ \ast }$-algebra, weakly completely continuous operators
Article copyright: © Copyright 1973 American Mathematical Society