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.

中文翻译：

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亚对称基本序列的二分法在 Garling 空间中的应用

我们在本文中的目的是为研究 Banach 空间（甚至更一般地说，在准 Banach 空间中）中的亚对称基本序列的结构做出贡献。为此，我们引入了定位的概念并开发了新工具，这些工具导致二分定理适用于具有次对称基的一般空间。为了说明如何使用这个二分定理，我们获得了某些类型空间中所有次对称序列的分类。更具体地说，我们证明 Garling 序列空间具有唯一的对称基本序列但没有对称基，并且这些空间具有亚对称基本序列的连续统。