l_p(X_k)中的联合逼近

Simultaneous approximation in l_p(X_k)

近年来,Banach空间中逼近性质的研究取得了较大的进展,徐士英,李冲等就Banach空间中的多种逼近问题展开了讨论,F.B.Saidi等曾研究了Bochner可积函数空间Lp(,μX)中联合逼近性质.就序列Banach空间lp(Xk)中的联合逼近性质进行了讨论,利用lp(Xk)中的性质及联合逼近的概念与性质得到了:设Yk为Xk的闭子空间(k=1,2,…),若Yk(k=1,2,…)自反,1<p<∞,则lp(Yk)为lp(Xk)中的N-联合逼近集.

The research on approximation Properties in Banach space has made a great progress in recent years. Many opproximation properties have been discussed by Shiying Xu and Chong Li etc, and the simultaneous approximation in Lebesgue-Bochner functional spaces lp（μ,X） studied by F. B. Saidi etc. The authors discuss the simultaneous approximation in the serial Banach space lp（Xk） . On the basis of the serial Banach space, the definition and the properties of the simultaneous approximation they get the result ： let Yk （k = 1, 2,…） be closed subspacesinXk（k = 1, 2,…） andYk（k = 1, 2,…） be reflexive,1 〈p 〈 ∞ , then lp（Yk） is N--simultaneously proximinal in lp（Xk）.