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

Abstract

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