Quotient normed cones
نویسندگان
چکیده
Given a normed cone (X , p) and a subcone Y, we construct and study the quotient normed cone (X/Y, p̃) generated by Y . In particular we characterize the bicompleteness of (X/Y, p̃) in terms of the bicompleteness of (X , p), and prove that the dual quotient cone ((X/Y )∗,‖ · ‖p̃,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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تاریخ انتشار 2003