# [Banach] Abstract of a paper by Oscar Valero

Dale Alspach alspach at www.math.okstate.edu
Wed Aug 2 16:54:42 CDT 2006

This is an announcement for the paper "Quotient normed cones" by
Oscar Valero.

Abstract: Given a normed cone $(X,p)$ and a subcone $Y,$ we construct
and study the quotient normed cone $(X/Y,\tilde{p})$ generated by
$Y$. In particular we characterize the bicompleteness of $(X/Y,\tilde{p})$
in terms of the bicompleteness of $(X,p),$ and prove that the dual
quotient cone $((X/Y)^{*},\|\cdot \|_{\tilde{p},u})$ can be identified
as a distinguished subcone of the dual cone $(X^{*},\|\cdot \|_{p,u})$.
Furthermore, some parts of the theory are presented in the general
setting of the space $CL(X,Y)$ of all continuous linear mappings
from a normed cone $(X,p)$ to a normed cone $(Y,q),$ extending
several well-known results related to open continuous linear mappings
between normed linear spaces.

Archive classification: Functional Analysis; General Topology

Mathematics Subject Classification: 54E35; 54E50; 54E99; 54H11

Remarks: 17 pages

The source file(s), mat01.cls: 37258 bytes, mathtimy.sty: 20 bytes,
pm2745new.tex: 58553 bytes, is(are) stored in gzipped form as
0607619.tar.gz with size 26kb. The corresponding postcript file has
gzipped size 61kb.

Submitted from: o.valero at uib.es

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http://front.math.ucdavis.edu/math.FA/0607619

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http://arXiv.org/abs/math.FA/0607619

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uget 0607619

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to: math at arXiv.org.