The Arrow-Barankin-Blackwell theorem in a dual space setting

摘要: In 1953 Arrow, Barankin, and Blackwell proved that, ifRn is equipped with its natural ordering ifF a closed convex subset ofRn, then the set of points inF that can be supported by strictly positive linear functionals dense in all efficient (maximal) ofF. Many generalizations this density result to infinite-dimensional settings have been given. note, we consider particular setting where setF contained topological dualY* partially ordered, nonreflexive normed spaceY, support are restricted either nonnegative or elements canonical embedding ofY inY*. Three alternative results obtained, two which generalize space-specific due Majumdar for dual system (Y,Y*)=(L1,L∞).