摘要
本文主要证明了如下一些结果:(1)设U,V是 Banach 空间X的两个子空间,U∩V是φ—可逼近的,则U+V是φ—可逼近集的充分必要条件是对任意f∈X,对应u∈U,v∈V使得(f-u-v-g)=φ(f-h)。(2)设U,V是两个线性子空间,U∩V是φ—可逼近集。对任意f∈X,存在唯一的u∈U,v∈V使得φ(f-u-v-g)=φ(f-h),则U+V是φ—Chebyshev 集。(3)设H是一个φ—很不逼近集,G是任意集,G+H≠X,则G+H为φ—很不逼近集。
In this paper,we get these main results: (1)If X is a Banach space,and U,V are two subspaces of X,then U+V is φ—proximinal set if and only if each f∈X corres u∈U,v∈V such that . (2)Let U,V be two subspaces in X,U∩V beφ-proximinal set.If each f∈X corres unique u∈U,v∈V such that, then U+V is φ—Chebyshev set. (3)If H is φ—very—non—proximinal set,G any set,G+H=X,then G+H is φ—very—non—proximinal set
关键词
φ逼近集
φ切比雪夫集
B空间
φ—Proximinal
φ—Chebyshev
φ—very—non—Proximinal
