Quotient Normed Cones

Proceedings Mathematical Sciences

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 (𝑋, 𝑝) and a subcone 𝑌, we construct and study the quotient normed cone $(X/Y,ilde{p})$ generated by 𝑌. In particular we characterize the bicompleteness of $(X/Y,ilde{p})$ in terms of the bicompleteness of (𝑋, 𝑝), 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 (𝑋, 𝑝) to a normed cone (𝑌, 𝑞), extending several well-known results related to open continuous linear mappings between normed linear spaces.

【 授权许可】

Unknown