论文标题
超紧凑型集的非线性方面
Nonlinear aspects of super weakly compact sets
论文作者
论文摘要
Banach空间子集的超弱紧凑性的概念是对弱紧凑性的增强，可以描述为局部版本的超反射性。 K. tu的最新结果表明，超弱紧凑型集合的闭合凸壳超级紧凑已消除了该理论进一步发展的主要障碍。在本文中，我们为超弱的紧凑性提供了各种结果，以表明该概念的巨大范围。我们还根据特殊树和图形的（非）嵌入性给出了超弱紧凑性的非线性表征。最后，我们以非超反射性Banach空间中超级紧凑的超紧凑型集合进行了一些相关示例。
The notion of super weak compactness for subsets of Banach spaces is a strengthening of the weak compactness that can be described as a local version of super-reflexivity. A recent result of K. Tu which establishes that the closed convex hull of a super weakly compact set is super weakly compact has removed the main obstacle to further development of the theory. In this paper we provide a variety of results around super weak compactness in order to show the great scope of this notion. We also give non linear characterizations of super weak compactness in terms of the (non) embeddability of special trees and graphs. We conclude with a few relevant examples of super weakly compact sets in non super-reflexive Banach spaces.
