In this note we extend to the quasi-reflexive setting the result of F. Baudier, N. Kalton and G. Lancien concerning the non-embeddability of the family of countably branching trees into reflexive Banach spaces whose Szlenk index and Szlenk index from the dual are both equal to the first infinite ordinal $\omega$. We also gather results linking these notions with the spreading models of the space.

中文翻译：

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关于可数分枝树家族到准自反 Banach 空间的嵌入性

在本笔记中，我们将 F. Baudier、N. Kalton 和 G. Lancien 关于可数分支树族不可嵌入到自反 Banach 空间的结果扩展到准自反设置，其 Szlenk 指数和 Szlenk 指数来自对偶都等于第一个无限序数 $\omega$。我们还收集将这些概念与空间的传播模型联系起来的结果。