# Similarity Techniques in the Spectral Analysis of Perturbed Operator Matrices

## TL;DR

This paper introduces a method for analyzing the spectral properties of unbounded perturbed operators, including differential operators with involution, using similarity techniques to handle matrix representations.

## Contribution

It develops the method of similar operators to study spectral properties of unbounded perturbed operators represented by matrices, including differential operators with involution.

## Key findings

- Applicable to differential operators with involution
- Provides a framework for spectral analysis of unbounded perturbed operators
- Extends similarity techniques to a broader class of operators

## Abstract

We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various differential operators with an involution, such as one-dimensional Dirac operators of a certain type.