Some locally convex spaces of continuous vector-valued functions over a completely regular space and their duals
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- by A. Katsaras
- Trans. Amer. Math. Soc. 216 (1976), 367-387
- DOI: https://doi.org/10.1090/S0002-9947-1976-0390733-9
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Abstract:
The strict, superstrict and the ${\beta _F}$ topologies are defined on a space A of continuous functions from a completely regular space into a Banach space E. Properties of these topologies are discussed and the corresponding dual spaces are identified with certain spaces of operator-valued measures. In case E is a Banach lattice, A becomes a lattice under the pointwise ordering and the strict and superstrict duals of A coincide with the spaces of all $\tau$-additive and all $\sigma$-additive functionals on A respectively.References
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Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 216 (1976), 367-387
- MSC: Primary 46E10
- DOI: https://doi.org/10.1090/S0002-9947-1976-0390733-9
- MathSciNet review: 0390733