We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(T*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent subsymmetric basic sequences and apply it to Su(T*)*. Finally, we provide a criterion for a subsymmetric sequence to be equivalent to the unit vector basis of some \({\ell _p}\) or c₀.

中文翻译：

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论次对称序列的唯一性和丰富性

我们探索具有次对称基础的空间中次对称基本序列的多样性。我们证明了 Tsirelson 原始 Banach 空间的次对称化 Su( T *) 提供了第一个已知的具有唯一次对称基本序列的空间示例，该序列另外也是非对称的。相比之下，我们为具有次对称基的空间提供了包含非等价次对称基本序列的连续统的准则，并将其应用于 Su( T *)*。最后，我们提供了一个标准，使次对称序列等效于某些\({\ell _p}\)或c ₀的单位向量基。