一类算子方程的解

J4 ›› 2012, Vol. 50 ›› Issue (03): 404-.

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Solutions to a Class of Operator Equation

XU Junlian^1,2, DU Hongke³

1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China;2. Department of Mathematics, Baoji University of Arts
and Sciences, Baoji 721013, Shaanxi Province, China;3. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China

Received:2011-06-13 Online:2012-05-26 Published:2012-05-28
Contact: DU Hongke E-mail:hkdu@snnu.edu.cn

Abstract

Abstract:

With the help of block operator matrix, the sufficient and necessary conditions for the existence of solutions to the operator equation AXB*+BX*A*=C and the representation of solutions were established. Especially, when 〖WTHX〗B〖WT〗 is an orthogonal projection P, the sufficient
and necessary conditions for the existence of solutions to the operator equation AXP+PX*A*=C and the representation of solutions were also given.

Key words: operator equation, MoorePenrose inverse, operator matrix, orthogonal projection

CLC Number:

O177.1

HU Dun-Lian, DU Hong-Ke. Solutions to a Class of Operator Equation[J].J4, 2012, 50(03): 404-.

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Solutions to a Class of Operator Equation

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