Duality in $B^{\ast }$-algebras
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- by Sheila A. McKilligan
- Proc. Amer. Math. Soc. 38 (1973), 86-88
- DOI: https://doi.org/10.1090/S0002-9939-1973-0326396-0
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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.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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