论文标题
菲尔普斯属性U和$ c（k）$空间
Phelps Property U and $C(K)$ spaces
论文作者
论文摘要
Banach Space $ y $的子空间$ x $具有$ \ textit {property u} $，每当$ x $上的每个连续线性功能都具有唯一的norm-norm-norm-norm-norm-norm-norm-prevelving（即hahn $ - $ banach）扩展到$ y $（Phelps，1960年）。在整个文档中，我们介绍并制定了一项系统的研究，对Banach Space $ x $和$ y $之间的$ \ textit {u-embeddings} $的存在，也就是说，等距嵌入$ x $的等距嵌入$ y $中的范围为y $，其范围是属性。我们为一般Banach空间和某些特定的设置提供结果，例如$ x $是有限维空间或$ c（k）$ - 空间。
A subspace $X$ of a Banach space $Y$ has $\textit{Property U}$ whenever every continuous linear functional on $X$ has a unique norm-preserving (i.e., Hahn$-$Banach) extension to $Y$ (Phelps, 1960). Throughout this document we introduce and develop a systematic study of the existence of $\textit{U-embeddings}$ between Banach spaces $X$ and $Y$, that is, isometric embeddings of $X$ into $Y$ whose ranges have property U. In particular, we are interested in the case that $Y=C(K)$, where $K$ is a compact Hausdorff topological space. We provide results for general Banach spaces and for some specific set-ups, such as $X$ being a finite-dimensional space or a $C(K)$-space.
