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On finite rank perturbations of definitizable operators |
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| Authors: | Tomas Ya. Azizov Jussi Behrndt Carsten Trunk |
| Affiliation: | a Department of Mathematics, Voronezh State University, Universitetskaya pl. 1, 394693 Voronezh, Russia b Technische Universität Berlin, Institut für Mathematik, MA 6-4,Straße des 17. Juni 136, D-10623 Berlin, Germany c Technische Universität Berlin, Institut für Mathematik, MA 6-3, Straße des 17. Juni 136, D-10623 Berlin, Germany |
| Abstract: | It was shown by P. Jonas and H. Langer that a selfadjoint definitizable operator A in a Krein space remains definitizable after a finite rank perturbation in resolvent sense if the perturbed operator B is selfadjoint and the resolvent set ρ(B) is nonempty. It is the aim of this note to prove a more general variant of this perturbation result where the assumption on ρ(B) is dropped. As an application a class of singular ordinary differential operators with indefinite weight functions is studied. |
| Keywords: | Definitizable operator Finite rank perturbation Krein space Differential operator Indefinite weight function |
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