Riesz Bases for p-Subordinate Perturbations of Normal Operators

Abstract

For p-subordinate perturbations of unbounded normal operators, the change of the spectrum is studied and spectral criteria for the existence of a Riesz basis with parentheses of root vectors are established. A Riesz basis without parentheses is obtained under an additional a priori assumption on the spectrum of the perturbed operator. The results are applied to two classes of block operator matrices.