October 16, 2025

Orthogonal Idempotents and Continuous Fredholm Operators under Perturbations

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 remain continuous when perturbed by orthogonal idempotents in Hilbert spaces.
The study characterizes the conditions required for these perturbations in Banach spaces.
Understanding these perturbations is crucial for broader applications in functional analysis.
Continuous systems in mathematics benefit from insights into the behavior of Fredholm operators.

Abstract

In the present work, authors presented characterization on continuity of Fredholm operators when perturbed by orthogonal idempotents in Banach space. In particular, authors show that these operators are continuous under pertubations in Hilbert spaces.

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Cite This Study

Nyaluke et al. (Sat,) studied this question.

synapsesocial.com/papers/68f04ad0e559138a1a06ecc4 https://doi.org/https://doi.org/10.65000/gx443b83

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