Perturbations of Krein spaces preserving the nonsingularity of the critical point infinity. (English) Zbl 0921.47033
Dijksma, A. (ed.) et al., Contributions to operator theory in spaces with an indefinite metric. The Heinz Langer anniversary volume on the occasion of his 60th birthday. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 106, 147-155 (1998).
Summary: We consider a nonnegative selfadjoint operator \(A\) in a Krein space such that \(\rho(A)\neq \emptyset\) and \(\infty\not\in c_s(A)\) (i.e. \(\infty\) is not a singular critical point of \(A\)). Then we show that these properties remain true for a certain perturbation of the operator, acting in a slightly perturbed Krein space. This result is applied to elliptic differential operators with indefinite weights and to certain difference operators.
For the entire collection see [Zbl 0901.00008].
For the entire collection see [Zbl 0901.00008].
MSC:
| 47B50 | Linear operators on spaces with an indefinite metric |
| 47B39 | Linear difference operators |
| 39A70 | Difference operators |
| 47F05 | General theory of partial differential operators |
| 46C20 | Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) |
