On a class of selfadjoint operators in Krein space and their compact perturbations (Q1106444)

The objectives are linear operators, selfadjoint with respect to the indefinite inner product of a Krein space. A selfadjoint operator is called definitizable if a certain real polynomial of it is non-negative. For a definitizable operator \textit{H. Langer} [Spektralfunktionen einer Klasse J-selfadjungierter Operatoren, Math. Nachr. 33, 107-120 (1967; Zbl 0147.121)] constructed a spectral function and established stability under a Macaev class perturbation. In the present paper the author extends these results to a wider class of selfadjoint operators, containing definitizable operators. Here definitizability is replaced by a growth condition of resolvents near the real axis and normality of the spectrum off the real axis.