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Open Access Research Article

An innovation analytical application of the proposed system of equations on Hilbert space

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pp. 1185–1196Vol. 28Issue 3-BApril 2025DOI: 10.47974/JIM-2207XML
Received:
10 Dec 2024
Published Online:
08 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2207
Pages:
1185–1196

Abstract

In the realm of Hilbert space, the applicability of the system of modeling equations in Operator Theory is investigated and considered. Recently, the interest in studying this type of systems has increased greatly. This article, employing the operators’ equations applicable to Hilbert space, deals with two systems of equations. It attempts to examine the required stipulations for the presence of a solution to this posed system. The first system comprises of two equations. For Λ and F that achieve regularity with non-invertibility, the general solution formula is investigated based on the Moore-Penrose inverse. Furthermore, the second system includes four equations having adjoint operators. Among the required stipulations, the operator attained self-adjoint attribute. The general solution formula is established based on the are regular of the operator when both Λ and F are regular. 

Keywords

Subject Classifications

Primary 46S4047A0547B02Secondary 47B15

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