Quotient normed cones
Given a normed cone (X, p) and a subconeY, we construct and study the quotient normed cone (X/Y,p) generated byY. In particular we characterize the bicompleteness of (X/Y, ‖·‖p,p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)*, ¦¦ · ‖·‖p,p) 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 spaceCL(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.
Volume 129 | Issue 5
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