Abstract and Applied Analysis

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, and Ge Dong

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 826564, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449679

Digital Object Identifier
doi:10.1155/2013/826564

Mathematical Reviews number (MathSciNet)
MR3132566

Citation

Fang, Xiaochun; Hou, Enran; Dong, Ge. 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 ${C}^{\ast}$ -Modules. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 826564, 8 pages. doi:10.1155/2013/826564. https://projecteuclid.org/euclid.aaa/1393449679


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