Riesz Bases for p-Subordinate Perturbations of Normal Operators

TL;DR

This paper investigates how p-subordinate perturbations affect the spectrum of normal operators and establishes spectral criteria for the existence of Riesz bases of root vectors, with applications to block operator matrices.

Contribution

It introduces new spectral criteria for Riesz bases under p-subordinate perturbations and provides conditions for bases without parentheses.

Findings

Spectral changes are characterized for p-subordinate perturbations.

Criteria for Riesz bases with parentheses are established.

Conditions for Riesz bases without parentheses are identified.

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.