An Investigation on Mathematical Modeling of Operators on The Hilbert Domain subjected to The Equality Theory

Salim Dawood  Mohsen; Ihsan Abdulsattar Awadh

doi:10.6180/jase.202512_28(12).0016

An Investigation on Mathematical Modeling of Operators on The Hilbert Domain subjected to The Equality Theory

Salim Dawood MohsenThis email address is being protected from spambots. You need JavaScript enabled to view it. and Ihsan Abdulsattar Awadh

Mustansiriyah University, College of Education, Department of mathematics, Baghdad, Iraq

Received: September 29, 2024
Accepted: April 4, 2025
Publication Date: April 24, 2025

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202512_28(12).0016

This work begins by presenting the essential and enough circumstances for the presence of the Hermitian solution to equations ΨXΦ + Φ^∗YΨ^∗ = Ω = Ψ^∗XΦ^∗+ ΦYΨ in the case where the operators are linear and bounded in a Hilbert space and in terms of the Moore-Penrose inverse, and when both Ψ and Φ have closed ranges. After that, the general solution form of this system is studied based on the generalized inverse.

Keywords: adjoint operator; systems of operator equations; generalized inverse; Moore-Penrose generalized inverse; Hermitian solution; general solution.

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