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Mat. Zametki, 2006, Volume 80, Issue 1, Pages 135–138 (Mi mz2789)  

This article is cited in 11 scientific papers (total in 11 papers)

Brief Communications

Similarity of Some $J$-Nonnegative Operators to Self-Adjoint Operators

A. S. Kostenko

Donetsk National University

Keywords: linear operator, self-adjoint operators, definitizable operator, Krein space, Hilbert space $L^2$ similarity criterion

DOI: https://doi.org/10.4213/mzm2789

Full text: PDF file (350 kB)
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English version:
Mathematical Notes, 2006, 80:1, 131–135

Bibliographic databases:

Received: 02.01.2006

Citation: A. S. Kostenko, “Similarity of Some $J$-Nonnegative Operators to Self-Adjoint Operators”, Mat. Zametki, 80:1 (2006), 135–138; Math. Notes, 80:1 (2006), 131–135

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Behrndt J., “On the spectral theory of singular indefinite Sturm-Liouville operators”, J. Math. Anal. Appl., 334:2 (2007), 1439–1449  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Wojtylak M., “A criterion for selfadjointness in Krein spaces”, Bull. Lond. Math. Soc., 40:5 (2008), 807–816  crossref  mathscinet  zmath  isi  scopus
    3. Karabash I., Kostenko A., “Indefinite Sturm-Liouville operators with the singular critical point zero”, Proc. Roy. Soc. Edinburgh Sect. A, 138:4 (2008), 801–820  crossref  mathscinet  zmath  isi  scopus
    4. I. M. Karabash, A. S. Kostenko, “On the Similarity of a $J$-Nonnegative Sturm–Liouville Operator to a Self-Adjoint Operator”, Funct. Anal. Appl., 43:1 (2009), 65–68  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Karabash I., Trunk C., “Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn $x$”, Proc. Roy. Soc. Edinburgh Sect. A, 139 (2009), 483–503  crossref  mathscinet  zmath  isi  elib  scopus
    6. Karabash I. M., Kostenko A. S., Malamud M. M., “The similarity problem for $J$-nonnegative Sturm-Liouville operators”, J. Differential Equations, 246:3 (2009), 964–997  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Karabash I.M., “Abstract Kinetic Equations with Positive Collision Operators”, Spectral Theory in Inner Product Spaces and Applications, Operator Theory Advances and Applications, 188, ed. Behrndt J. Forster KH. Langer H. Trunk C., Birkhauser Verlag Ag, 2009, 175–195  mathscinet  zmath  isi
    8. Karabash I.M., “A Functional Model, Eigenvalues, and Finite Singular Critical Points for Indefinite Sturm-Liouville Operators”, Topics in Operator Theory, Vol 2: Systems and Mathematical Physics, Operator Theory Advances and Applications, 203, ed. Ball J. Bolotnikov V. Helton J. Rodman L. Spitkovsky I., Birkhauser Verlag Ag, 2010, 247–287  crossref  mathscinet  zmath  isi
    9. Markov V.G., “Nekotorye svoistva neznakoopredelennykh operatorov shturma-liuvillya”, Matematicheskie zametki YaGU, 19:1 (2012), 44–59  mathscinet  zmath  elib
    10. Kostenko A., “The Similarity Problem for Indefinite Sturm-Liouville Operators and the Help Inequality”, Adv. Math., 246 (2013), 368–413  crossref  mathscinet  zmath  isi  elib  scopus
    11. Pyatkov S.G., “Existence of Maximal Semidefinite Invariant Subspaces and Semigroup Properties of Some Classes of Ordinary Differential Operators”, Oper. Matrices, 8:1 (2014), 237–254  crossref  mathscinet  zmath  isi  elib  scopus
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