论文标题
锤型指标的几何形状及其嵌入在Banach空间中
The geometry of Hamming-type metrics and their embeddings into Banach spaces
论文作者
论文摘要
在反射性Banach空间的类别中，我们证明了对Bi-Lipschitz不变式的渐近造成的标准表征，该类别涉及$ k $ subsets of $ \ mathbb {n} $的指标。我们将这种表征应用于表明，可分离，反射性和渐近性 - $ C_0 $ BANACH空间是非孔子分析的。最后，我们介绍了渐近造成的$ C_0 $属性的放松，称为渐近序列 - $ C_0 $属性，这是对锤子序列序列的等效性嵌入性的部分障碍。我们介绍了渐近续顺序$ C_0 $的空间的示例。尤其是$ t^*（t^*）$是渐近 - 安排 - $ c_0 $，其中$ t^*$是tsirelson的原始空间。
Within the class of reflexive Banach spaces, we prove a metric characterization of the class of asymptotic-$c_0$ spaces in terms of a bi-Lipschitz invariant which involves metrics that generalize the Hamming metric on $k$-subsets of $\mathbb{N}$. We apply this characterization to show that the class of separable, reflexive, and asymptotic-$c_0$ Banach spaces is non-Borel co-analytic. Finally, we introduce a relaxation of the asymptotic-$c_0$ property, called the asymptotic-subsequential-$c_0$ property, which is a partial obstruction to the equi-coarse embeddability of the sequence of Hamming graphs. We present examples of spaces that are asymptotic-subsequential-$c_0$. In particular $T^*(T^*)$ is asymptotic-subsequential-$c_0$ where $T^*$ is Tsirelson's original space.
