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2013 Solutions to the System of Operator Equations A 1 X = C 1 , X B 2 = C 2 , and A 3 X B 3 = C 3 on Hilbert C * -Modules
Xiaochun Fang, Enran Hou, Ge Dong
Abstr. Appl. Anal. 2013(SI45): 1-8 (2013). DOI: 10.1155/2013/826564

Abstract

We study the solvability of the system of the adjointable operator equations A 1 X = C 1 , X B 2 = C 2 , and A 3 X B 3 = C 3 over Hilbert C * -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.

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Xiaochun Fang. Enran Hou. Ge Dong. "Solutions to the System of Operator Equations A 1 X = C 1 , X B 2 = C 2 , and A 3 X B 3 = C 3 on Hilbert C * -Modules." Abstr. Appl. Anal. 2013 (SI45) 1 - 8, 2013. https://doi.org/10.1155/2013/826564

Information

Published: 2013
First available in Project Euclid: 26 February 2014

MathSciNet: MR3132566
Digital Object Identifier: 10.1155/2013/826564

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI45 • 2013
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