[Banach] Abstract of a paper by Jeremy J. Becnel

[Dale Alspach]

This is an announcement for the paper "About countably-normed spaces"
by Jeremy J. Becnel.


Abstract: Here we present an overview of countably normed spaces. In
particular, we discuss the main topologies---weak, strong, inductive, and
Mackey---placed on the dual of a countably normed spaces and discuss the
sigma fields generated by these topologies. In particlar, we show that the
strong, inductive, and Mackey topologies are equivalent under reasonable
conditions. Also we show that all four topologies induce the same Borel
field under certain conditions. The purpose in mind is to provide the
background material for many of the results used in White Noise Analysis.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46A11

Remarks: 23 pages, 0 figures, Background material for White Noise Analysis

The source file(s), NuclearSpace.bbl: 1198 bytes, NuclearSpace.tex:
1472 bytes, borel.tex: 5271 bytes, cns.tex: 16479 bytes, compare.tex:
6600 bytes, conclusion.tex: 4430 bytes, inductive.tex: 6567 bytes,
nuclear.sty: 4578 bytes, strong.tex: 17400 bytes, tvs.tex: 14418 bytes,
weak.tex: 3536 bytes, is(are) stored in gzipped form as 0407200.tar.gz
with size 23kb. The corresponding postcript file has gzipped size 103kb.

Submitted from: beck at math.lsu.edu

The paper may be downloaded from the archive by web browser from URL

 http://front.math.ucdavis.edu/math.FA/0407200

 or

 http://arXiv.org/abs/math.FA/0407200

or by email in unzipped form by transmitting an empty message with
subject line

	 uget 0407200


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	 get 0407200

 to: math at arXiv.org.