Abstract
We consider two systems of adjointable operator equations \(A_{1}X=C_{1}, XB_{2}=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}\) and \(A_{1}X=C_{1}, A_{2}X=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}\) over the Hilbert \(C^{*}\)-modules. Necessary and sufficient conditions for the existence and the expressions of the general solutions to those systems are established.
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Acknowledgements
This research was supported by the grants from the youth funds of Natural Science Foundation of Hebei Province (A2012403013), the Education Department Foundation of Hebei Province (QN2015218), and the Natural Science Foundation of Hebei Province (A2015403050).
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Cao, NB., Zhang, YP. (2018). The General Solutions to Some Systems of Adjointable Operator Equations. In: Kar, S., Maulik, U., Li, X. (eds) Operations Research and Optimization. FOTA 2016. Springer Proceedings in Mathematics & Statistics, vol 225. Springer, Singapore. https://doi.org/10.1007/978-981-10-7814-9_8
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DOI: https://doi.org/10.1007/978-981-10-7814-9_8
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