The spectrum of diagonal perturbation of weighted shift operator

TL;DR

This paper characterizes the spectrum of weighted shift operators on a Hilbert space when subjected to diagonal perturbations, providing insights into their spectral properties.

Contribution

It offers a detailed description of how diagonal perturbations affect the spectrum of weighted shift operators, a novel analysis in operator theory.

Findings

Spectral characterization of perturbed weighted shift operators

Conditions under which the spectrum changes due to diagonal perturbations

New theoretical insights into spectral stability

Abstract

This paper provides a description of the spectrum of diagonal perturbation of weighted shift operator acting on a separable Hilbert space.