论文标题
在子因子的铺路尺寸上
On the paving size of a subfactor
论文作者
论文摘要
给定有限琼斯指数的II $ _1 $因子$ n \ subset m $，$ [m：n] <\ infty $，我们证明，对于任何$ f \ subset m $有限和$ \ varepsilon> 0 $的任何$ f \ subset m $ \ lceil 4 [m：n] \ varepsilon^{ - 2} \ rceil $ juptions $ p_1，...，p_r \ in n $ in n $，这样，$ \ | \ | \ sum_ {i = 1}^r p_ixp_i-e_ e _ e _ e _ e _ {n'\ cap m}（x） m}（x）\ | $，$ \ forall x \ in f $（其中$ \lceilβ\ rceil $表示最小整数$ \ geqβ$）。我们考虑了$ n \ subset m $的一系列相关不变式，通常称为{\ it铺路尺寸}。
Given an inclusion of II$_1$ factors $N\subset M$ with finite Jones index, $[M:N]<\infty$, we prove that for any $F\subset M$ finite and $\varepsilon >0$, there exists a partition of $1$ with $r\leq \lceil 16\varepsilon^{-2}\rceil$ $\cdot \lceil 4 [M:N]\varepsilon^{-2}\rceil$ projections $p_1, ..., p_r\in N$ such that $\|\sum_{i=1}^r p_ixp_i - E_{N'\cap M}(x)\|\leq \varepsilon \|x-E_{N'\cap M}(x)\|$, $\forall x\in F$ (where $\lceil β\rceil$ denotes the least integer $\geq β$). We consider a series of related invariants for $N\subset M$, generically called {\it paving size}.
