摘要
We prove the following main result: Let X be a normed linear space,fn ∈ X*\{θ},Hn = {x ∈ X: fn(x) = l},n = 0, 1,2,...Then w* - limfn = f0 iff H0 lim inf Hn and θ limsup Hn; when X is a reflexive Banach space, lim ||fn - f0|| = 0. If and only if θ w-limsup Hn Ho It simplifies the related results in [1].
在本文中，我们证明下述主要结果：（ｉ）设Ｘ是赋范线性空间，ｆｎ∈Ｘ*＼｛θ｝Ｈｎ｛ｘ∈Ｘ：ｆｎ（ｘ）＝１｝，ｎ＝０，１，２，…，则ｗ*－ｌｉｍｆｎ=ｆｏ当且仅当Ｈｏ ｌｉｍｉｎｆ Ｈｎ且θ ｌｉｍｓｕｐＨｎ；（ｉｉ）当Ｘ是自反的Ｂａｎａｃｈ空间时，ｌｉｍ｜｜ｆｎ－ｆｏ｜｜＝０当且仅当θ ｗ－ｌｉｍｓｕｐ Ｈｎ Ｈ０．
