$C(M)$上自伴随矩阵的近似对角化
Approximate diagonalization of self--adjoint matrices over $C(M)$
摘要：
设$M$是紧T2空间.本文证明了$C(M)$上的每一个自伴随矩阵都是近似可对角化的当且仅当$\dim M\le 2$和$\HO^2(M,\mathbb Z)\cong 0$ .利用这个结果，我们证明了当$M$是紧度量空间时，$C(M)$上的每个酉矩阵都是近似可对角化的当且仅当$\dim M\le 2$，$\HO^1(M,\mathbb Z)\cong\HO^2(M,\mathbb Z)\cong 0$.
英文摘要：
Let $M$ be a compact Hausdorff space. We prove that in this paper, every self--adjoint matrix over $C(M)$ is approximately diagonalizable iff $\dim M\le 2$ and $\HO^2(M,\mathbb Z)\cong 0$. Using this result, we show that every unitary matrix over $C(M)$ is approximately diagonalizable iff $\dim M\le 2$, $\HO^1(M,\mathbb Z)\cong\HO^2(M,\mathbb Z)\cong 0$ when $M$ is a compact metric space.
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