巢代数的大扰动

Kenneth R. Davidson
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引用次数: 0

摘要

让 $\mathcal{M}$ 和 $\mathcal{N}$ 是可分离的希尔伯特空间上的嵌套。如果两个巢代数的距离小于 1($d(\mathcal{T}(\mathcal{M}),\mathcal{T}(\mathcal{N}))<1$),则嵌套的距离小于 1($d(\mathcal{M},\mathcal{N})<1$)。如果嵌套之间的距离小于 1,那么嵌套代数是相似的,即存在一个可逆的 $S$,使得 $S\mathcal{M} = \mathcal{N}$,从而 $S\mathcal{T}(\mathcal{M})S^{-1} = \mathcal{T}(\mathcal{N})$。然而,也有一些嵌套距离大于 1 的例子,它们的嵌套代数相差 1 个距离。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Large Perturbations of Nest Algebras
Let $\mathcal{M}$ and $\mathcal{N}$ be nests on separable Hilbert space. If the two nest algebras are distance less than 1 ($d(\mathcal{T}(\mathcal{M}),\mathcal{T}(\mathcal{N})) < 1$), then the nests are distance less than 1 ($d(\mathcal{M},\mathcal{N})<1$). If the nests are distance less than 1 apart, then the nest algebras are similar, i.e. there is an invertible $S$ such that $S\mathcal{M} = \mathcal{N}$, so that $S \mathcal{T}(\mathcal{M})S^{-1} = \mathcal{T}(\mathcal{N})$. However there are examples of nests closer than 1 for which the nest algebras are distance 1 apart.
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