Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximately diagonalizing matrices over C(Y)   Let $X$ be a compact metric space which is locally absolutely retract and let
$\phi: C(X)\to C(Y, M_n)$ be a unital homomorphism, where $Y$ is a compact
metric space with ${\rm dim}Y\le 2.$ It is proved that there exists a sequence
of $n$ continuous maps $\alfa_{i,m}: Y\to X$ ($i=1,2,...,n$) and a sequence of
sets of mutually orthogonal rank one projections $\{p_{1, m},
p_{2,m},...,p_{n,m}\}\subset C(Y, M_n)$ such that $$ \lim_{m\to\infty}
\sum_{i=1}^n f(\alfa_{i,m})p_{i,m}=\phi(f) for all f\in C(X). $$
  This is closely related to the Kadison diagonal matrix question. It is also
shown that this approximate diagonalization could not hold in general when
${\rm dim}Y\ge 3.$

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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: quant-ph