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Equivalence of topologies and Borel fields for countably-Hilbert spaces


Author: Jeremy J. Becnel
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
Published electronically: August 12, 2005
MathSciNet review: 2176027
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • Jeremy J. Becnel, About Countably-Normed Spaces, http://xxx.lanl.gov/abs/math.FA/0407200, 23 pages, 2004.
  • I. M. Gel′fand and G. E. Shilov, Generalized functions. Vol. 2. Spaces of fundamental and generalized functions, Academic Press, New York-London, 1968. Translated from the Russian by Morris D. Friedman, Amiel Feinstein and Christian P. Peltzer. MR 0230128
  • I. M. Gel’fand and N. Ya. Vilenkin, Generalized functions. Vol. 4: Applications of harmonic analysis, Academic Press, New York - London, 1964, 1964. Translated by Amiel Feinstein. MR 0173945
  • Gottfried Köthe, Topological vector spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 159, Springer-Verlag New York Inc., New York, 1969. Translated from the German by D. J. H. Garling. MR 0248498
  • Hui-Hsiung Kuo, White noise distribution theory, Probability and Stochastics Series, CRC Press, Boca Raton, FL, 1996. MR 1387829
  • A. P. Robertson and W. J. Robertson, Topological vector spaces, Cambridge Tracts in Mathematics and Mathematical Physics, No. 53, Cambridge University Press, New York, 1964. MR 0162118
  • Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469
  • Yau-Chuen Wong, Introductory theory of topological vector spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 167, Marcel Dekker, Inc., New York, 1992. With a chapter by Mau-Hsiang Shih [Mou Hsiang Shih]. MR 1198892

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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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.