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June 21, 2026Asian-European Journal of Mathematics0 citations

Connections between polynomially Riesz and Fredholm elements in Banach algebras with closed inessential ideals

Key Points

This paper aims to analyze the relationship between polynomially Riesz and Fredholm elements in Banach algebras through spectral perturbations.
Developed spectral analysis for Fredholm theory incorporating polynomially Riesz elements.
Evaluated essential spectra of perturbed elements due to polynomial perturbations.
Investigated connections between Riesz and Fredholm elements using closed inessential ideals.
Established that polynomially Riesz perturbations affect the structure of Fredholm elements in Banach algebras.
Demonstrated connections between Riesz and Fredholm elements enhanced by polynomial perturbations.
Identified key properties of inessential ideals influencing the essential spectra in this context.

Abstract

The purpose of this paper is to establish some spectral analysis in Fredholm theory that incorporates the concept of polynomially Riesz elements perturbation. Furthermore, we use the results we have gathered to evaluate the impact of certain essential spectra of perturbed elements through this type of perturbation.This kind of perturbation allows us to reinterpret the structure of Fredholm elements in terms of polynomially Riesz elements and the ideal of Riesz operators in Banach algebras. Finally, we investigate the connection between Riesz and Fredholm elements by perturbing polynomially Riesz elements through a closed inessential ideal.

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