Real positive solutions of operator equations $ AX = C $ and $ XB = D $-Reference-Cited by-同舟云学术

Real positive solutions of operator equations $ AX = C $ and $ XB = D $

Published:2023 Issue:7 Volume:8 Page:15214-15231
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zhang Haiyan¹,Dou Yanni²,Yu Weiyan³

Affiliation:

1. School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China

2. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China

3. College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

Abstract

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

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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