Abstract
In this paper, we consider the solvability of the system of two operator equations \(AX=C\) and \(XB=D\) in the framework of Hilbert \(C{{}^{*}}\)-modules as well as the existence of Hermitian and positive solutions. We also provide formulae for the general forms of such solutions.
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Acknowledgements
The authors would like to thank the anonymous reviewers for their comments and suggestions. The first author is supported by the project titled: Operator matrices, numerical range and applications, Serbian Academy of Sciences and Arts, no.O-23-19 and by the National Natural Science Foundation of China (11971294). The first and the second author are supported by the Ministry of Education, Science and Technological Development, Republic of Serbia (451-03-68/2020-14/200124). The third author is supported by the National Natural Science Foundation of China (11671261, 11971136) and a grant from the Science and Technology Commission of Shanghai Municipality (18590745200).
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Communicated by Mox S. Moslehian.
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Nikolov Radenković, J., Cvetković-Ilić, D. & Xu, Q. Solvability of the system of operator equations \(AX=C\), \(XB=D\) in Hilbert \(C{{}^{*}}\)-modules. Ann. Funct. Anal. 12, 32 (2021). https://doi.org/10.1007/s43034-021-00110-3
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DOI: https://doi.org/10.1007/s43034-021-00110-3