Approximate diagonalization of self-adjoint matrices over \(C(M)\)

zbMATH Open1289.46083arXiv1002.3962MaRDI QIDQ2853227

Yifeng Xue

Publication date: 18 October 2013

Published in: Functional Analysis, Approximation and Computation (Search for Journal in Brave)

Abstract: Let $M$ be a compact Hausdorff space. We prove that in this paper, every self--adjoint matrix over $C(M)$ is approximately diagonalizable iff $dimMle2$ and $H{O}^2(M,mathbbZ)cong0$. Using this result, we show that every unitary matrix over $C(M)$ is approximately diagonalizable iff $dimMle2$, $H{O}^1(M,mathbbZ)congH{O}^2(M,mathbbZ)cong0$ when $M$ is a compact metric space.

Full work available at URL: https://arxiv.org/abs/1002.3962

zbMATH Keywords

vector bundleapproximately diagonaldimension of compact Hausdorff space

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05)

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