Weighted inner weak group inverse

Year 2026, Issue: Advanced Online Publication, 1 - 16

Dijana Mosic , Gregor Doinar , Bojan Kuzma , Janko Marovt

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

Supporting Institution

The first author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, grant No. 451-03-47/2023-01/200124. The research of Dolinar, Kuzma, and Marovt was supported in part by the Slovenian Research Agency, ARRS (research programs P1-0285 and P1-0288, and research project N1-0210).

References

• [1] M. Arslan and E. Du¨ndar, Rough ideal convergence in 2-normed spaces, Turkish Journal of Science 9 (1), 6-18, 2024