On domains of powers of linear operators and finite rank perturbations

Azizov, Tomas Ya; Behrndt, Jussi GND; Philipp, Friedrich; Trunk, Carsten GND

Let S and T be linear operators in a linear space such that S T. In this note an estimate for the codimension of domSn in domTn in terms of the codimension of domS in domT 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 selfadjoint definitizable operators in Krein spaces.

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Azizov, Tomas Ya / Behrndt, Jussi / Philipp, Friedrich / et al: On domains of powers of linear operators and finite rank perturbations. 2007.

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