Fredholm Perturbation of Spectra of $2\times 2$ Upper Triangular Matrix

TL;DR

This paper characterizes how various spectra of a 2x2 upper triangular operator matrix are affected by Fredholm perturbations, providing a comprehensive spectral analysis relevant to mathematical physics and quantum mechanics.

Contribution

It offers a new characterization of Fredholm perturbations for multiple spectra of 2x2 upper triangular operator matrices, extending spectral perturbation theory.

Findings

Characterization of Fredholm perturbation effects on Weyl spectrum

Analysis of essential and other spectra under perturbations

Extension of spectral perturbation results to upper triangular matrices

Abstract

As we knew, study the perturbation theory of spectra of operator is a very important project in mathematics physics, in particular, in quantum mechanics. In this paper, we characterize the Fredholm perturbation for the Weyl spectrum, essential spectrum, spectrum, left spectrum, right spectrum, lower semi-Fredholm spectrum, upper semi-Weyl spectrum and lower semi-Weyl spectrum of upper triangular operator matrix $M_{C}=({cc} A&C 0&B)$.