Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative Gelfand Duality and Applications I: The Existence of
  invariant subspaces   Gelfand duality between unital commutative C*-algebras and Compact Hausdorff
spaces is extended to all unital C*-algebras, where the dual objects are what
we call compact Hausdorff quantum spaces. We apply this result to obtain, a
characterization of unitary groups of C*-algebras, and, for arbitrary bounded
Hilbert space operators, (i) A spectral theorem cum continuous functional
calculus, and (ii) A proof of the general Invariant Subspace Theorem. Also
described is a nonabelian generalization of Pontryagin duality of abelian
locally compact groups.

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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int