论文标题
限制Chebyshev中心$ l_1 $ - 先知的空间
Restricted Chebyshev centers in $L_1$-predual spaces
论文作者
论文摘要
在本文中，我们为在$ l_ {1} $的紧凑子集中存在限制的Chebyshev中心提供了必要和足够的条件 - 在$ L_ {1} $ - 预定空间的封闭凸子集中的$ l_ {1} $ - 预定空间。我们还提供了$ L_ {1} $的几何表征，即按照以下方式限制的Chebyshev半径。一个真正的Banach Space $ x $是$ l_ {1} $ - 仅当每个非空的有限子集$ f $ $ x $的$ x $和闭合的convex子集$ v $ $ x $，$ x $，$ rad_ {v}（f）= rad_ {x}}（x}}（x}}（x}（x}）） $ rad_ {v}（f）$，$ cent_ {x}（f）$和$ d（v，cent_ {x}（f））$，是$ x $ in $ x $的$ f $的chebyshev半径，有限的chebyshev radius $ f $ in $ v $ in $ v $ in $ f $ f $ f $ f $ f $ in $ f $ in $ x in $ x in $ Cent_ {x}（f）$。此外，我们明确描述了在紧凑的Hausdorff空间上实现的连续功能的$ m $ summ和$ m $ summ和的Chebyshev中心。
In this paper, we provide a necessary and sufficient condition for the existence of a restricted Chebyshev center of a compact subset of an $L_{1}$-predual space in a closed convex subset of the $L_{1}$-predual space. We also provide a geometrical characterization of an $L_{1}$-predual space in terms of the restricted Chebyshev radius in the following manner. A real Banach space $X$ is an $L_{1}$-predual space if and only if for each non-empty finite subset $F$ of $X$ and closed convex subset $V$ of $X$, $rad_{V}(F) = rad_{X}(F) + d(V, cent_{X}(F))$, where we denote $rad_{X}(F)$, $rad_{V}(F)$, $cent_{X}(F)$ and $d(V, cent_{X}(F))$ to be the Chebyshev radius of $F$ in $X$, the restricted Chebyshev radius of $F$ in $V$, the set of Chebyshev centers of $F$ in $X$ and the distance between the sets $V$ and $cent_{X}(F)$ respectively. Furthermore, we explicitly describe the Chebyshev centers of closed bounded subsets of an $M$-summand in the space of real-valued continuous functions on a compact Hausdorff space.
