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Abstract and Applied Analysis
Volume 2013, Article ID 826564, 8 pages
http://dx.doi.org/10.1155/2013/826564
Research Article

Solutions to the System of Operator Equations , , and on Hilbert -Modules

1Department of Mathematics, Tongji University, Shanghai 200092, China
2Department of Basic Teaching, Jianqiao College, Shanghai 201319, China

Received 12 September 2013; Accepted 4 November 2013

Academic Editor: Antonio M. Peralta

Copyright © 2013 Xiaochun Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the solvability of the system of the adjointable operator equations , , and over Hilbert -modules. We give necessary and sufficient conditions for the existence of a solution and a positive solution of the system. We also derive representations for a general solution and a positive solution to this system. The above results generalize some recent results concerning the equations for operators with closed ranges.