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This is a Quantitative Study study.

October 16, 2025

Fredholmness Conditions for Operators Perturbed by Orthogonal Idempotents in Banach Spaces

KNK.W NyalukeJaramogi Oginga Odinga University of Science and Technology BOBenard OkeloJaramogi Oginga Odinga University of Science and Technology OOOmolo OngatiJaramogi Oginga Odinga University of Science and Technology

Key Points

Fredholm operators can maintain their properties under certain conditions when perturbed.
Key conditions for retaining fredholmness include specific characteristics of the perturbing idempotents.
The study focuses on operators within infinite dimensional complex hilbert spaces.
Understanding these conditions is important for advancing operator theory in banach spaces.

Abstract

Let H be an infinite dimensional complex Hilbert space and F01(H) the set of all Fredholm operators perturbed by orthogonal idempotents in Banach space. In the present paper, we determine the conditions under which Fredholm operators retain Fredholmness when perturbed by orthogonal idempotents in Banach spaces.

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