On a class of selfadjoint operators in Krein space and their compact perturbations
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.
growth condition of resolvents near the real axis
normality of the spectrum off the real axis
scientific article; zbMATH DE number 4061978
scientific article