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
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Submitted from: o.valero@uib.es
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