论文标题
可驯服和罗森塔尔当地凸出的空间
Tameness and Rosenthal type locally convex spaces
论文作者
论文摘要
由罗森塔尔（Rosenthal）著名的$ l^1 $ dichothome在Banach空间，海顿定理（Haydon's Therorem）以及最近关于驯服动态系统的著作中的动机，我们介绍了驯服的本地凸面空间。这是Rosenthal Banach空间的天然局部凸类似物（对于任何有限的序列都包含弱的Cauchy子序列）。我们的方法是基于驯服子集的出生学，而驯养子集则与最终的分散性密切相关。这导致了以下结果： $ \ bullet $扩展了海顿对Rosenthal Banach空间的特征，表明LCS $ E $是驯服的，如果每个弱星，紧凑的，等效的凸子集的$ e^{*} $是强烈的封闭convex hull，则是其极端的convex hull，其极端要点是其极端的点，即\ edline {\ rm {co \，}}}（k）$ for $ e^{*} $的每个弱星compart compact equincont equincont equincont equientinuul $ \ bullet $ $ e $是tame iff，没有等同于广义$ l^{1} $ - 序列的限制顺序； $ \ bullet $增强W.M.的一些结果关于罗森塔尔的二分法； $ \ bullet $应用Davis-Figiel-Johnson-Pelczyński（dfjp）技术，一个人可能表明，每个驯服的操作员$ t \ colon e \ to f $ to f $ to lcs $ e $与Banach Space $ f $之间的f $都可以通过Tame（即Rossenthal）Banach Space进行。
Motivated by Rosenthal's famous $l^1$-dichotomy in Banach spaces, Haydon's theorem, and additionally by recent works on tame dynamical systems, we introduce the class of tame locally convex spaces. This is a natural locally convex analogue of Rosenthal Banach spaces (for which any bounded sequence contains a weak Cauchy subsequence). Our approach is based on a bornology of tame subsets which in turn is closely related to eventual fragmentability. This leads, among others, to the following results: $\bullet$ extending Haydon's characterization of Rosenthal Banach spaces, by showing that a lcs $E$ is tame iff every weak-star compact, equicontinuous convex subset of $E^{*}$ is the strong closed convex hull of its extreme points iff $\overline{\rm{co\,}}^{w^{*}}(K) = \overline{\rm{co\,}}(K)$ for every weak-star compact equicontinuous subset $K$ of $E^{*}$; $\bullet$ $E$ is tame iff there is no bounded sequence equivalent to the generalized $l^{1}$-sequence; $\bullet$ strengthening some results of W.M. Ruess about Rosenthal's dichotomy; $\bullet$ applying the Davis-Figiel-Johnson-Pelczyński (DFJP) technique one may show that every tame operator $T \colon E \to F$ between a lcs $E$ and a Banach space $F$ can be factored through a tame (i.e., Rosenthal) Banach space.
