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Operator Solutions of the Multi–valued Operator Equation A=BXC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A = BXC$$\end{document}Operator Solutions of the Multi–valued Operator Equation A=BXC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A = BXC$$\end{document}A. Sandovici
被引：0
作者：
Adrian Sandovici
[1
]
机构：
[1] “Gheorghe Asachi” Technical University of Iaşi,Department of Mathematics and Informatics
关键词：
Linear space;
Linear operator;
Linear relation;
Operator equation;
Primary 47A06;
Secondary 47A05.;
D O I：
10.1007/s40840-025-01836-2
中图分类号：
学科分类号：
摘要：
Assume that A, B and C are three linear relations on certain linear spaces. The main objective of this note is to present some necessary and sufficient conditions for the existence of the solutions X of the operator equation A=BXC\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$A = BXC$$\end{document}. The obtained characterizations extend and complete some known operator factorization results due to R.G. Douglas, Z. Sebestyén and D. Popovici.
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