Perturbations of definitizable operators in a space with an indefinite metric (Q1094651)

Perturbations of definitizable operators in Krein space are studied. First, the convergence of resolvents and spectral functions is discussed if a sequence of definitizable operators converges in a general sense. Second, for the operational calculus relating to continuous functions, various convergence of operator functions are studied. At last, the relation for the convergence of the sequence of resolvents and that of one-parameter unitary groups is studied. The main theorems of this paper can be regarded as the generalization of the results for self-adjoint operators in Hilbert space.