Trees and branches in Banach spaces
Trees and branches in Banach spaces
复制标题
Banach 空间中的树木和树枝
DOI：
10.1090/s0002-9947-02-02984-7
复制
发表时间：
2000
影响因子：
1.3
通讯作者：
T. Schlumprecht
中科院分区：
文献类型：
--
作者：
E. Odell;T. Schlumprecht
考虑了无穷维渐近结构的概念。这一概念是在Banach空间上的树和枝的基础上发展起来的。空间X上的每一棵可数无限可数分枝树T都假定有一个具有某种性质的分支。证明了X可以嵌入到具有FDD(Ei)的空间中，使得X中几乎是(Ei)的跳过分块的归一化序列都具有这一性质。作为我们工作的一个应用，我们证明了如果X是一个可分自反Banach空间，并且对于某个10，存在X的一个有限余维子空间，它的C2+e嵌入到有限维空间的L p和中。
An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree T of a certain type on a space X is presumed to have a branch with some property. It is shown that then X can be embedded into a space with an FDD (E i ) so that all normalized sequences in X which are almost a skipped blocking of (E i ) have that property. As an application of our work we prove that if X is a separable reflexive Banach space and for some 1 0, there exists a subspace of X having finite codimension which C 2 + e embeds into the l p sum of finite dimensional spaces.