Equivalence of topologies and Borel fields for countably-Hilbert spaces
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- by Jeremy J. Becnel PDF
- Proc. Amer. Math. Soc. 134 (2006), 581-590 Request permission
Abstract:
We examine the main topologies—weak, strong, and inductive—placed on the dual of a countably-normed space and the $\sigma$-fields generated by these topologies. In particular, we prove that for certain countably-Hilbert spaces the strong and inductive topologies coincide and the $\sigma$-fields generated by the weak, strong, and inductive topologies are equivalent.References
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Additional Information
- Jeremy J. Becnel
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- Email: beck@math.lsu.edu
- Received by editor(s): September 2, 2004
- Published electronically: August 12, 2005
- Communicated by: Jonathan M. Borwein
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 581-590
- MSC (2000): Primary 57N17; Secondary 60H40
- DOI: https://doi.org/10.1090/S0002-9939-05-08219-5
- MathSciNet review: 2176027