论文标题
超级紧凑性定量的应用
Applications of the quantification of super weak compactness
论文作者
论文摘要
我们介绍了针对Banach空间中有界线性操作员和子集定义的超弱非碰撞性$γ$的度量，这些量度允许陈述和证明是Hilbert生成的空间子空间的Banach空间的表征。超级弱的紧凑性和$γ$的使用对这些Banach空间的结构进行了启示，并补充了Argyros，Fabian，Farmaki，Godefroy，Hájek，Hájek，Montesinos，\ Line Break Troyanski和Zizizler在此主题上。一种特殊的相对较弱的紧凑型集，即均匀的弱空集，起着重要作用，并与Banach-Saks型特性展示了连接。
We introduce a measure of super weak noncompactness $Γ$ defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert generated space. The use of super weak compactness and $Γ$ casts light on the structure of these Banach spaces and complements the work of Argyros, Fabian, Farmaki, Godefroy, Hájek, Montesinos,\linebreak Troyanski and Zizler on this subject. A particular kind of relatively super weakly compact sets, namely uniformly weakly null sets, plays an important role and exhibits connections with Banach-Saks type properties.
