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商绍强 《数学物理学报(B辑英文版)》2021,(2):461-474
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 and pn→p uniformly on each bounded subset of X*;(3)for anyα∈(0,1),there exists a ball-covering{B(x*i,n,Ti,n)}∞i=1 of(X*,pn)such that it isα-off the origin and xi,n*∈Gnn.Moreover,we also prove that if Xi is a Gateaux differentiability space,then there exist a real numberα>0 and a ball-covering(B)i of Xi such that(B)i isα-off the origin if and only if there exist a real numberα>0 and a ball-covering B of l∞(Xi)such that(B)isα-off the origin. 相似文献
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以Banach空间的一般凸集为研究对象,将Banach空间的凸性研究推广到了内部非空的凸集上.打破了从单位球出发研究Banach空间几何的具有局限性的研究方法,给出了严格凸集的若干特征刻画及性质,并得到了严格凸集和光滑集之间的对偶定理. 相似文献
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