Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Reducing of the Invariant Semidefinite Subspace Problem for Krein
  Noncontraction to such a Problem for Krein Isometry   Definition. Let J be a period-2 unitary operator (some people say J is
reflection operator or reflection symmetry) and U be a linear operator.
  If U^*JU = J (resp. U^*JU >= J) then U is said to be J-isometry (resp.
J-noncontraction).
  If U^*JU >= J and UJU^* >= J) then U is said to be J-binoncontraction).
  Theorem. If every J-isometry has nontrivial positive invariant subspace then
every J-noncontraction has such a subspace.
  Theorem. If every J-binoncontractive J-isometry has maximal positive
invariant subspace then every J-noncontraction has such a subspace.
  The article text is the complete text of the author's report on 15-th
Voronezh Winter Mathematical School, p 119 (see. VINITI 16.12.81, N 5691-81).
But in that time the presented construtions and theorems seemed to be rather
curious observations. Now the situattion is changing (see e.g. math.DS/9908169)

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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th