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July 2019 Solutions to some systems of adjointable operator equations over Hilbert $C^*$-modules
Zahra Niazi Moghani, Mahnaz Khanehgir
Tbilisi Math. J. 12(3): 93-107 (July 2019). DOI: 10.32513/tbilisi/1569463236

Abstract

In this paper, by using operator matrix techniques, we present necessary and sufficient conditions for the existence of a solution to the system of equations $AXD+FX^{*}B=C,$ $GXF^{*}+FX^{*}G^{*}=H$ for adjointable operators between Hilbert $C^*$-modules, and derive an expression for the general solution to the system. We establish necessary and sufficient conditions for the existence of a solution to the system of adjointable operator equations $AXF=H_{1},$ $CXD=H_{2},$ $BXD=H_{3}$ over Hilbert $C^*$-modules. Some of the findings of this paper extend some known results in the literature.

Citation

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Zahra Niazi Moghani. Mahnaz Khanehgir. "Solutions to some systems of adjointable operator equations over Hilbert $C^*$-modules." Tbilisi Math. J. 12 (3) 93 - 107, July 2019. https://doi.org/10.32513/tbilisi/1569463236

Information

Received: 4 November 2017; Accepted: 25 July 2019; Published: July 2019
First available in Project Euclid: 26 September 2019

zbMATH: 07172327
MathSciNet: MR4012385
Digital Object Identifier: 10.32513/tbilisi/1569463236

Subjects:
Primary: 47A62
Secondary: ‎15A09, ‎15A24‎, 46L08

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

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Vol.12 • No. 3 • July 2019
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