Proceedings Mathematical Sciences | |
Quotient Normed Cones | |
Oscar Valero1  | |
[1] Departamento de Ciencias Matemáticas e Informática, Edificio Anselm Turmeda, Universidad de las Islas Baleares, 0 Palma, Spain$$ | |
关键词: Normed cone; extended quasi-metric; continuous linear mapping; bicompleteness; quotient cone; dual.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
Given a normed cone (ð‘‹, ð‘) and a subcone ð‘Œ, we construct and study the quotient normed cone $(X/Y,ilde{p})$ generated by ð‘Œ. In particular we characterize the bicompleteness of $(X/Y,ilde{p})$ in terms of the bicompleteness of (ð‘‹, ð‘), and prove that the dual quotient cone $((X/Y)^∗,|cdot|_{ilde{p},u})$ can be identified as a distinguished subcone of the dual cone $(X^∗,|cdot|_{ilde{p},u})$. 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 (ð‘‹, ð‘) to a normed cone (ð‘Œ, ð‘ž), extending several well-known results related to open continuous linear mappings between normed linear spaces.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040506729ZK.pdf | 248KB | download |