Quotient normed cones

2006/07/25 by Oscar Valero, Valero, Oscar
Mathematics · #54E35 #54E50 #54E99 #54H11 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #math.FA #math.GN #msc:54E35 #msc:54E50 #msc:54E99 #msc:54H11

paper · pdf · doi:10.48550/arxiv.math/0607619

17 pages

arxiv created 2006/07/25 · arxiv updated 2009/12/01

Abstract

Given a normed cone (X,p) and a subcone Y, we construct and study the quotient normed cone (X/Y,p) generated by Y. In particular we characterize the bicompleteness of (X/Y,p) in terms of the bicompleteness of (X,p), and prove that the dual quotient cone ((X/Y)^*,‖⋅ ‖_p,u) can be identified as a distinguished subcone of the dual cone (X^*,‖⋅ ‖_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.

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