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

2010/02/21 by Xue, Yifeng
#46L05 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1002.3962

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 dim M≤ 2 and \HO²(M,\mathbb Z)≅ 0. Using this result, we show that every unitary matrix over C(M) is approximately diagonalizable iff dim M≤ 2, \HO¹(M,\mathbb Z)≅\HO²(M,\mathbb Z)≅ 0 when M is a compact metric space.

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