Dual spaces of weighted spaces

Author:
W. H. Summers

Journal:
Trans. Amer. Math. Soc. **151** (1970), 323-333

MSC:
Primary 46.25

DOI:
https://doi.org/10.1090/S0002-9947-1970-0270129-5

MathSciNet review:
0270129

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Abstract: The topological duals of a large class of weighted spaces of continuous functions are characterized as spaces of Radon measures which can be factored into a product of a weight function and a bounded Radon measure. We next obtain a representation for a base for the equicontinuous subsets of these dual spaces and for the extremal points of the members of this base. Finally, among other applications, these ideas make possible an extension of the representation theorem for biequicontinuous completed tensor products of weighted spaces obtained by the author in an earlier paper.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0270129-5

Keywords:
Weighted spaces of continuous functions,
strict topology,
Radon measure,
equicontinuous sets,
extremal points,
Nachbin family,
factorization,
biequicontinuous completed tensor product,
Mackey space

Article copyright:
© Copyright 1970
American Mathematical Society