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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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