THE BALL-COVERING PROPERTY ON DUAL SPACES AND BANACH SEQUENCE SPACES  

作　　者：Shaoqiang SHANG 商绍强(College of Mathematical Sciences,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]College of Mathematical Sciences,Harbin Engineering University,Harbin 150001,China

出　　处：《Acta Mathematica Scientia》2021年第2期461-474,共14页数学物理学报（B辑英文版）

基　　金：supported by the“China Natural Science Fund”under grant 11871181;the“China Natural Science Fund”under grant 12026423.

摘　　要：In this paper,we prove that(X,p)is separable if and only if there exists a w^(*)-lower semicontinuous norm sequence{p_(n)}_(n=1)^(∞)of(X^(*),p)such that(1)there exists a dense subset G_(n)of X^(*)such that p_(n)is Gateaux differentiable on G_(n)and dp_(n)(Gn_(n))■X for all n∈N;(2)p_(n)≤p and p_(n)→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^(*),p_(n))such that it isα-off the origin and x_(i,n)^(*)∈Gn_(n).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^(∞)(X_(i))such that(B)isα-off the origin.

关 键 词：Ball-covering property separable space Gateaux differentiable point weak^(*)exposed point 

分 类 号：O177.2[理学—数学]