论文标题
在二元组合的空间上
On the spaces dual to combinatorial Banach spaces
论文作者
论文摘要
我们提出了与组合Banach空间的双重相关的准巴纳赫空间。更确切地说，对于$ω$的有限子集的紧凑型家庭$ \ MATHCAL {F} $，我们定义了Quasi-norm $ \ cdot \ cdot \ cdot \ cdot \ rvert^\ Mathcal {f} $，其banach Inlevelope是$ \ Mathcal of Mathcal of Combinatorial空间的双重标准。这样的准标准似乎比双重规范容易得多，但是它们引起的准巴纳奇空间与双重空间共享许多属性。我们表明，大型家庭（从洛佩兹 - 阿巴德和托德斯维克的意义上）引起的准桶空间是$ \ ell_1 $饱和的，没有Schur属性。特别是，这适用于Schreier家庭。
We present quasi-Banach spaces which are closely related to the duals of combinatorial Banach spaces. More precisely, for a compact family $\mathcal{F}$ of finite subsets of $ω$ we define a quasi-norm $\lVert \cdot \rVert^\mathcal{F}$ whose Banach envelope is the dual norm for the combinatorial space generated by $\mathcal{F}$. Such quasi-norms seem to be much easier to handle than the dual norms and yet the quasi-Banach spaces induced by them share many properties with the dual spaces. We show that the quasi-Banach spaces induced by large families (in the sense of Lopez-Abad and Todorcevic) are $\ell_1$-saturated and do not have the Schur property. In particular, this holds for the Schreier families.
