论文标题
关于黑斯廷斯对林定理几乎通勤矩阵的方法
On Hastings' approach to Lin's Theorem for Almost Commuting Matrices
论文作者
论文摘要
林的定理指出，对于所有$ε> 0 $，都有$Δ> 0 $，以便对于所有$ n \ geq 1 $，如果自偶会收缩$ a，b \ in m_n（\ m athbb {c}）$ coblesy $ \ \ \ | [a，b] m_n（\ mathbb {c}）$，带有$ [a'，b'] = 0 $和$ \ | a-a'\ |，\ | b-b'\ |<ε$。我们介绍了ARXIV中该方法的充分解释和纠正的细节：0808.2474，这是Lin定理的第一个提供渐近估计值的版本。 我们还将此方法应用于$ b $是普通矩阵的情况，频谱位于$ \ mathbb {c} $的一些不错的一维子集中。
Lin's theorem states that for all $ε> 0$, there is a $δ> 0$ such that for all $n \geq 1$ if self-adjoint contractions $A,B \in M_n(\mathbb{C})$ satisfy $\|[A,B]\|< δ$ then there are self-adjoint contractions $A',B' \in M_n(\mathbb{C})$ with $[A',B']=0$ and $\|A-A'\|,\|B-B'\|<ε$. We present fully explained and corrected details of the approach in arXiv:0808.2474, which was the first version of Lin's theorem to provide asymptotic estimates. We also apply this method to the case where $B$ is a normal matrix with spectrum lying in some nice 1-dimensional subset of $\mathbb{C}$.
