Weighted G-Outer Inverse of Banach Spaces Operators

Mosić, Dijana

doi:10.1080/01630563.2022.2051186

Numerical Functional Analysis and Optimization

2022

DOI: 10.1080/01630563.2022.2051186

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Weighted G-Outer Inverse of Banach Spaces Operators

Dijana Mosić

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Weighted generalized core–EP inverse

Mosić,

Marovt

2024

Linear and Multilinear Algebra

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Weighted generalized core–EP inverse

Mosić,

Marovt

2024

Linear and Multilinear Algebra

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Extensions of G-outer inverses

Mosic,

Stanimirovic,

Ciric

2023

Filomat

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Our first objective is to present equivalent conditions for the solvability of the system of matrix equations ADA = A, D= B and CAD = C, where D is unknown, A, B,C are of appropriate dimensions, and to obtain its general solution in terms of appropriate inner inverses. Our leading idea is to find characterizations and representations of a subclass of inner inverses that satisfy some properties of outer inverses. A G-(B,C) inverse of A is defined as a solution of this matrix system. In this way, G-(B,C) inverses are defined and investigated as an extension of G-outer inverses. One-sided versions of G-(B,C) inverse are introduced as weaker kinds of G-(B,C) inverses and generalizations of one-sided versions of G-outer inverse. Applying the G-(B,C) inverse and its one-sided versions, we propose three new partial orders on the set of complex matrices. These new partial orders extend the concepts of G-outer (T, S)-partial order and one-sided G-outer (T, S)-partial orders.

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Weighted G-Outer Inverse of Banach Spaces Operators

Cited by 2 publications

References 42 publications

Weighted generalized core–EP inverse

Weighted generalized core–EP inverse

Extensions of G-outer inverses

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