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An invariant subspace theorem


Author: John Daughtry
Journal: Proc. Amer. Math. Soc. 49 (1975), 267-268
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1975-0365176-9
MathSciNet review: 0365176
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Abstract: If $ AY - YA$ has rank one for some compact $ Y$, then $ A$ has a nontrivial invariant subspace.


References [Enhancements On Off] (What's this?)

  • [1] V. J. Lomonosov, Invariant subspaces for operators commuting with compact operators, Funkcional. Anal. i Priložen 7 (1973), 55-56. (Russian) MR 0420305 (54:8319)
  • [2] D. G. Luenberger, Invertible solutions to the operator equation $ TA - BT = C$, Proc. Amer. Math. Soc. 16 (1965), 1226-1229. MR 32 #1562. MR 0184088 (32:1562)
  • [3] H. Radjavi and P. Rosenthal, Invariant subspaces, Ergebnisse der Math., Vol. 77, Springer-Verlag, New York, 1973, p. 156. MR 0367682 (51:3924)
  • [4] J. P. Williams, On the range of a derivation, Pacific J. Math. 38 (1971), 273-279. MR 46 #7923. MR 0308809 (46:7923)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0365176-9
Keywords: Invariant subspace, Lomonosov's theorem, linear operator equation
Article copyright: © Copyright 1975 American Mathematical Society

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