$L^{\Phi}(I,X)$中的最佳同时逼近

Best Simultaneous Approximation in $L^{\Phi}(I,X)$

中文关键词:  同时  逼近  Orlicz空间.

英文关键词:simultaneous  approximation  Orlicz spaces.

中文摘要:

      设$X$为Banach空间，$\Phi$为Orlicz空间,记$L^{\Phi}(I,X)$为定义在单位区间$I$上,取值于$X$的$\Phi$-可积函数构成的空间,赋该空间Luxemburg范数.对$X$的一个闭子集,提出了$f_{1},f_{2},\ldots\,f_{m}\in L^{\Phi}(I,X)$到$L^{\Phi}(I,G)$的一种距离公式$dist_{\Phi}(f_{1},f_{2},\ldots\,f_{m},L^{\Phi}(I, G))$,进一步给出了$L^{\Phi}(I,G)$对$L^{\Phi}(I,X)$最佳同时逼近的存在性及特征定理.

英文摘要:

      Let $X$ be a Banach space and $\Phi$ be an Orlicz function. Denote by $L^{\Phi}(I,X)$ the space of $X$-valued $\Phi$-integrable functions on the unit interval $I$ equipped with the Luxemburg norm. For $f_{1},f_{2},\ldots,f_{m}\in L^{\Phi}(I,X)$, a distance formula $\dist_{\Phi}(f_{1},f_{2},\ldots,f_{m},L^{\Phi}(I, G))$ is presented, where $G$ is a close subspace of $X$. Moreover, some existence and characterization results concerning the best simultaneous approximation of $L^{\Phi}(I,G)$ in $L^{\Phi}(I,X)$ are given.