Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Stability I: Completely Positive Maps   We show that for every "locally finite" unit-preserving completely positive
map P acting on a C*-algebra, there is a corresponding *-automorphism \alpha of
another unital C*-algebra such that the two sequences P, P^2,P^3,... and
\alpha, \alpha^2,\alpha^3,... have the same {\em asymptotic} behavior. The
automorphism \alpha is uniquely determined by P up to conjugacy. Similar
results hold for normal completely positive maps on von Neumann algebras, as
well as for one-parameter semigroups.
  These results can be viewed as operator algebraic counterparts of the
classical Perron-Frobenius theorem on the structure of square matrices with
nonnegative entries.

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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: stat