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In this paper,we prove that(X,p)is separable if and only if there exists a w*-lower semicontinuous norm sequence{pn}n=1∞of(X*,p)such that(1)there exists a dense subset Gnof X*such that pnis Gateaux differentiable on Gnand dpn(Gnn)■X for all n∈N;(2)pn≤p an