Abstract
Let S and T be linear operators in a linear space such that S ⊂ T. In this note an estimate for the codimension of dom S n in dom T n in terms of the codimension of dom S in dom T is obtained. An immediate consequence is that for any polynomial p the operator p(S) is a finite-dimensional restriction of the operator p(T) whenever S is a finite-dimensional restriction of T. The general results are applied to a perturbation problem of self-adjoint definitizable operators in Krein spaces.
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