An invariant subspace theorem
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- by John Daughtry PDF
- Proc. Amer. Math. Soc. 49 (1975), 267-268 Request permission
Abstract:
If $AY - YA$ has rank one for some compact $Y$, then $A$ has a nontrivial invariant subspace.References
- V. I. Lomonosov, Invariant subspaces of the family of operators that commute with a completely continuous operator, Funkcional. Anal. i Priložen. 7 (1973), no. 3, 55–56 (Russian). MR 0420305
- David G. Luenberger, Invertible solutions to the operator equation $TA-BT=C$, Proc. Amer. Math. Soc. 16 (1965), 1226–1229. MR 184088, DOI 10.1090/S0002-9939-1965-0184088-0
- Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77, Springer-Verlag, New York-Heidelberg, 1973. MR 0367682, DOI 10.1007/978-3-642-65574-6
- J. P. Williams, On the range of a derivation, Pacific J. Math. 38 (1971), 273–279. MR 308809, DOI 10.2140/pjm.1971.38.273
Additional Information
- © Copyright 1975 American Mathematical Society
- 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