[Banach] Abstract of a paper by Jeremy J. Becnel
alspach at www.math.okstate.edu
Tue Jul 13 07:24:07 CDT 2004
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
or by email in unzipped form by transmitting an empty message with
or in gzipped form by using subject line
to: math at arXiv.org.
More information about the Banach