On Compact Perturbations of Locally Definitizable Selfadjoint Relations in Krein Spaces |
| |
Authors: | Jussi Behrndt Peter Jonas |
| |
Affiliation: | (1) Fachbereich Mathematik, MA 6-4, Technische Universität Berlin, Str. d. 17. Juni 136, D-10623 Berlin, Germany |
| |
Abstract: | The aim of this paper is to prove two perturbation results for a selfadjoint operator A in a Krein space which can roughly be described as follows: (1) If is an open subset of and all spectral subspaces for A corresponding to compact subsets of have finite rank of negativity, the same is true for a selfadjoint operator B in for which the difference of the resolvents of A and B is compact. (2) The property that there exists some neighbourhood of such that the restriction of A to a spectral subspace for A corresponding to is a nonnegative operator in is preserved under relative 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. |
| |
Keywords: | Primary 47B50 Secondary 47A55 47B40 |
本文献已被 SpringerLink 等数据库收录! |