论文标题
Laakso图的公制嵌入到Banach空间中
Metric embeddings of Laakso graphs into Banach spaces
论文作者
论文摘要
令$ x $为Banach Space，它不是超反射的。然后，对于每种$ n \ ge1 $和$ \ varepsilon> 0 $，我们展示了Laakso Graph $ \ Mathcal {l} _n $的公制嵌入到$ x $中，失真小于$ 2+\ varepsilon $，并带有$ l_1 [0,1] $ 4/3 $ 4/3 $。 $ \ Mathcal {l} _2 $（分别是钻石图$ d_2 $）嵌入$ \ MATHCAL {0,1] $的嵌入变形至少为$ 9/8 $（分别分别为$ 5/4 $）。
Let $X$ be Banach space which is not super-reflexive. Then, for each $n\ge1$ and $\varepsilon>0$, we exhibit metric embeddings of the Laakso graph $\mathcal{L}_n$ into $X$ with distortion less than $2+\varepsilon$ and into $L_1[0,1]$ with distortion $4/3$. The distortion of an embedding of $\mathcal{L}_2$ (respectively, the diamond graph $D_2$) into $L_1[0,1]$ is at least $9/8$ (respectively, $5/4$).
