Weak topologies on subspaces of $C(S)$
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- by Joel H. Shapiro PDF
- Trans. Amer. Math. Soc. 157 (1971), 471-479 Request permission
Abstract:
Let $S$ be a locally compact Hausdorff space, $E$ a linear subspace of $C(S)$. It is shown that the unit ball of $E$ is compact in the strict topology if and only if both of the following two conditions are satisfied: (1) $E$ is the Banach space dual of $M(S)/{E^0}$ in the integration pairing, and (2) the bounded weak star topology on $E$ coincides with the strict topology. This result is applied to several examples, among which are ${l^\infty }$ and the space of bounded analytic functions on a plane region.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 157 (1971), 471-479
- MSC: Primary 46E10
- DOI: https://doi.org/10.1090/S0002-9947-1971-0415285-1
- MathSciNet review: 0415285