论文标题
$ C_0（i）$的扭曲总和
Twisted sums of $c_0(I)$
论文作者
论文摘要
Banach Space $ x $带有$ C_0（κ）$的扭曲总和的论文研究属性。我们首先证明了这种扭曲的总和的表示定理，除其他外，我们还将获得以下内容：（a）$ c_0（i）$和$ c_0（κ）$的扭曲总和是$ \ ell_ \ ell_ \ infty（κ）$的子空间，或者是$ C_0（κ^+）$; （b）在假设$ [\ mathfrak p = \ mathfrak c] $下，当$ k $是合适的corson compact，可分离的罗斯塔尔紧凑型或有限高度的散落的紧凑型，有$ c（k）$的扭曲和$ c_0（κ）$，这不是连续函数的异构函数的$ c_0（κ）$； （c）当$ x $是lindenstrauss空间时，所有这些扭曲的总和都是lindenstrauss的空间，当$ x = c（k）$带有$ k $ convex时，$ g $ - 空格，这表明benyamini的结果是最佳的； （d）当$ x $是一个带有属性（$ \ star $）的多面体空间时，它们是同构的多面体，该空间解决了Castillo和Papini的问题。
The paper studies properties of twisted sums of a Banach space $X$ with $c_0(κ)$. We first prove a representation theorem for such twisted sums from which we will obtain, among others, the following: (a) twisted sums of $c_0(I)$ and $c_0(κ)$ are either subspaces of $\ell_\infty(κ)$ or trivial on a copy of $c_0(κ^+)$; (b) under the hypothesis $[\mathfrak p = \mathfrak c]$, when $K$ is either a suitable Corson compact, a separable Rosenthal compact or a scattered compact of finite height, there is a twisted sum of $C(K)$ with $c_0(κ)$ that is not isomorphic to a space of continuous functions; (c) all such twisted sums are Lindenstrauss spaces when $X$ is a Lindenstrauss space and $G$-spaces when $X=C(K)$ with $K$ convex, which shows tat a result of Benyamini is optimal; (d) they are isomorphically polyhedral when $X$ is a polyhedral space with property ($\star$), which solves a problem of Castillo and Papini.
