On Compact Perturbations of Locally Definitizable Selfadjoint Relations in Krein Spaces
| dc.contributor.author | Behrndt, Jussi | |
| dc.contributor.author | Jonas, Peter | |
| dc.date.accessioned | 2021-12-17T10:05:44Z | |
| dc.date.available | 2021-12-17T10:05:44Z | |
| dc.date.issued | 2003-02-28 | |
| dc.description.abstract | The aim of this paper is to prove two perturbation results for a selfadjoint operator A in a Krein space H which can roughly be described as follows: (1) If Δ is an open subset of R, and all spectral subspaces for A corresponding to compact subsets of Δ have finite rank of negativity, the same is true for a selfadjoint operator B in H for which the difference of the resolvents of A and B is compact. (2) The property that there exists some neighbourhood Δ∞ of ∞ such that the restriction of A to a spectral subspace for A corresponding to Δ∞ is a nonnegative operator in H, is preserved under relative Sp perturbations in form sense if the resulting operator is again selfadjoint. The assertion (1) is proved for selfadjoint relations A and B. (1) and (2) generalize some known results. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15509 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14282 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | selfadjoint operators in Krein spaces | en |
| dc.subject.other | compact perturbations | en |
| dc.subject.other | definitizable operators | en |
| dc.subject.other | spectral points of positive and negative type | en |
| dc.subject.other | selfadjoint linear relations | en |
| dc.title | On Compact Perturbations of Locally Definitizable Selfadjoint Relations in Krein Spaces | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2003, 07 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 47B50 Operators on spaces with an indefinite metric | en |
| tub.subject.msc2000 | 47A55 Perturbation theory | en |