Some Properties Related with Spectral Compact Operators on Banach Spaces

Abstract

Spectral compact operators play a crucial role in functional analysis, particularly in

understanding the spectral behavior of linear operators on Banach spaces. These

operators exhibit properties that make their spectra more manageable compared to

general bounded operators. This paper explores key spectral properties of compact

operators in Banach spaces, including the discreteness of the spectrum, the finite-

dimensionality of eigenspaces, the spectral radius formula, and perturbation properties. We also discuss applications of these operators in solving integral equations,

differential equations, and data analysis.