次对称基序列的二分法及其在Garling空间中的应用
A dichotomy for subsymmetric basic sequences with applications to Garling spaces
摘要：
我们在这篇文章中的目的是有助于结构的次对称基本序列在巴拿赫空间（甚至，更一般地说，在准巴拿赫空间）的研究。为此，我们引入定位的概念，并开发新的工具，导致二分法定理，持有一般空间的次对称基地。作为如何使用这个二分法定理的一个例子，我们得到了在某些类型的空间中的所有次对称序列的分类。更具体地说，我们证明了Garling数列空间有唯一的对称基列但没有对称基，并且这些空间有次对称基列的连续统。
英文摘要：
Our aim in this article is to contribute to the study of the structure of subsymmetric basic sequences in Banach spaces (even, more generally, in quasi-Banach spaces). For that we introduce the notion of positioning and develop new tools which lead to a dichotomy theorem that holds for general spaces with subsymmetric bases. As an illustration of how to use this dichotomy theorem we obtain the classification of all subsymmetric sequences in certain types of spaces. To be more specific, we show that Garling sequence spaces have a unique symmetric basic sequence but no symmetric basis and that these spaces have a continuum of subsymmetric basic sequences.
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