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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
Posted:
August 12, 2005
MathSciNet review:
2176027
Full-text PDF Free Access
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Abstract: We examine the main topologies--weak, strong, and inductive--placed on the dual of a countably-normed space and the  -fields generated by these topologies. In particular, we prove that for certain countably-Hilbert spaces the strong and inductive topologies coincide and the  -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
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08219-5
PII:
S 0002-9939(05)08219-5
Received by editor(s):
September 2, 2004
Posted:
August 12, 2005
Communicated by:
Jonathan M. Borwein
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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