On the solutions of operator equation CAX = C = XAC

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Deng, Chunyuan

关键词: Operator equation;    Inner inverse;    General solution;   

DOI  :  10.1016/j.jmaa.2012.09.033

来源: Elsevier

【 摘 要 】

In this paper, we find the explicit solutions of the equation CAX = C = XAC for linear bounded operators on Hilbert spaces, where the unknown operator X is called the inverse of A along C. This solution is expressed in terms of the inner inverses of the operators AC and CA. From these formulas we derive necessary and sufficient conditions for the solution to be unique. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free