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Research Article | Open Access

Real positive solutions of operator equations A X = C and X B = D

Haiyan Zhang1( ), Yanni Dou2, Weiyan Yu3
School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China
College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
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Abstract

In this paper, we mainly consider operator equations A X = C and X B = D in the framework of Hilbert space. A new representation of the reduced solution of A X = C is given by a convergent operator sequence. The common solutions and common real positive solutions of the system of two operator equations A X = C and X B = D are studied. The detailed representations of these solutions are provided which extend the classical closed range case with a short proof.

Keywords

reduced solutionreal positive solutionoperator equation
CLC number: 15A09, 47A05

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 15214-15231
DOI: 10.3934/math.2023777

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Cite this article:
Zhang H, Dou Y, Yu W. Real positive solutions of operator equations A X = C and X B = D. AIMS Mathematics, 2023, 8(7): 15214-15231. https://doi.org/10.3934/math.2023777

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Received: 30 December 2022
Revised: 15 April 2023
Accepted: 19 April 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)