Weighted inner weak group inverse

Objective & Hypothesis:Solving a system of operator equations which extends early studied systems of equations, we present the notion of weighted inner weak group inverse for bounded linear operators between two Hilbert spaces.

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Key Findings & Data:In this way, we generalize the concepts of the weighted MP weak group inverse for rectangular matrices and the 1WG inverse for square matrices.

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Conclusion & Impact:The weighted inner weak group inverse is applied in solving certain linear equations and in representing their general solution forms.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:weighted MP weak group inverse · weighted weak group inverse · inner inverse

Abstract

Solving a system of operator equations which extends early studied systems of equations, we present the notion of weighted inner weak group inverse for bounded linear operators between two Hilbert spaces. In this way, we generalize the concepts of the weighted MP weak group inverse for rectangular matrices and the 1WG inverse for square matrices. We give many characterizations and expressions for weighted inner weak group inverse. The operator matrix form of weighted inner weak group inverse is established. We consider the inner weak group inverse of operators as a special case of the weighted inner weak group inverse. The weighted inner weak group inverse is applied in solving certain linear equations and in representing their general solution forms.

Keywords

weighted MP weak group inverse weighted weak group inverse inner inverse MP weak group inverse Hilbert space

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Cite This Article

Mosic, D., Doinar, G., Kuzma, B., Marovt, J. (2026). Weighted inner weak group inverse. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 2. https://doi.org/10.15672/hujms.1438702

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