Abstract
For nonnegative operators in Kreĭnn spaces we give conditions for the preservation of the nonemptiness of the resolvent set and the preservation of the regularity of critical points under relatively form bounded perturbations.
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References
R.V. Akopyan, On the theory of the spectral function of a J-nonnegative operator, Izv. Akad. Nauk Armyanskoi SSR, 13(1978), 114–121.
B. Ćurgus, On the regularity of the critical point infinity of definitizable operators, Integral Equations and Operator Theory, 8(1985), 462–488.
B. Ćurgus and B. Najman, A Krečn space approach to elliptic eigenvalue problems with indefinite weights, Differential and Integral Equations, 7(1994), 1241–1252.
B. Ćurgus and B. Najman, Perturbations of range, Proc. Amer. Math. Soc. (to appear)
P. Jonas, Compact perturbations of definitizable operators. II, J. Operator Theory, 8(1982), 3–18.
P. Jonas, On a problem of the perturbation theory of selfadjoint operators in Kreĭnn space, J. Operator Theory, 25(1991), 183–211.
P. Jonas, On the spectral theory of operators associated with perturbed Klein-Gordon and wave type equations, J. Operator Theory, 29(1993), 207–224.
P. Jonas and H. Langer, Some questions in the perturbations theory of J-nonnegative operators in Kreĭnn space, Math. Nachr. 114(1983), 205–226.
T. Kato, Perturbation theory for linear operators, Springer Verlag, New York, 1966.
H. Langer, Verallgemeinerte Resolventen eines J-nichtnegativen Operators mit endlichem Defekt, J. Functional Analysis, 8(1971), 287–320.
H. Langer, Spectral functions of definitizable operators in Kreĭnn spaces, Functional Analysis, Proceedings of a conference held at Dubrovnik, Lecture Notes in Mathematics, 948, Springer Verlag, Berlin-Heidelberg-New York, 1982, 1–46.
J.-L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, Vol. I, Paris, 1968.
B. Najman, Solution of a differential equation in a scale of spaces, Glasnik Matematički, 14(1979), 119–127.
B. Najman, Trace class perturbations and scattering theory for the equations of Klein-Gordon type, Glasnik Matematički, 15(1980), 79–86.
B. Najman, Spectral properties of the operators of Klein-Gordon type, Glasnik Matematički, 15(1980), 97–112.
M. Reed, B. Simon, Methods of Modern Mathematical Physics, II: Fourier Analysis, Selfadjointness, Academic Press, New York, San Francisco, London 1975.
K. Veselić, On spectral properties of a class of J-selfadjoint operators, I, Glasnik Matematički, 7(1972), 229–247.
K. Veselić, On spectral properties of a class of J-selfadjoint operators, II, Glasnik Matematički, 7(1972), 249–254.
K. Veselić, A spectral theory of the Klein-Gordon equation involving a homogeneous electric field, J. Operator Theory, 25 (1991), 319–330.
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Dedicated to Heinz Langer on the occasion of his 60th birthday
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Jonas, P. (1998). Riggings and relatively form bounded perturbations of nonnegative operators in Kreĭn spaces. In: Dijksma, A., Gohberg, I., Kaashoek, M.A., Mennicken, R. (eds) Contributions to Operator Theory in Spaces with an Indefinite Metric. Operator Theory Advances and Applications, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8812-7_13
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DOI: https://doi.org/10.1007/978-3-0348-8812-7_13
Publisher Name: Birkhäuser, Basel
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