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Ukrainian Mathematical Journal

, Volume 67, Issue 5, pp 795–813 | Cite as

On Decompositions of a Scalar Operator into a Sum of Self-Adjoint Operators with Finite Spectrum

  • V. I. Rabanovych
Article
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We consider the problem of classification of nonequivalent representations of a scalar operator λI in the form of a sum of k self-adjoint operators with at most n 1 , . . . ,n k points in their spectra, respectively. It is shown that this problem is *-wild for some sets of spectra if (n 1 , . . . ,n k ) coincides with one of the following k -tuples: (2, . . . , 2) for k ≥ 5, (2, 2, 2, 3), (2, 11, 11), (5, 5, 5), or (4, 6, 6). It is demonstrated that, for the operators with points 0 and 1 in the spectra and k ≥ 5, the classification problems are *-wild for every rational λϵ 2 [2, 3].

Keywords

Hilbert Space Irreducible Representation English Translation Scalar Operator Matrix Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. I. Rabanovych
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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