Quotient normed cones
| dc.creator | Valero, Oscar | |
| dc.date | 2006-07-25 | |
| dc.date.accessioned | 2026-07-07T07:20:53Z | |
| dc.date.available | 2026-07-07T07:20:53Z | |
| dc.description | 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. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0607619 | |
| dc.identifier | http://arxiv.org/abs/math/0607619 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115108 | |
| dc.subject | Functional Analysis | |
| dc.subject | General Topology | |
| dc.subject | 54E35; 54E50; 54E99; 54H11 | |
| dc.title | Quotient normed cones | |
| dc.type | text |