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.

中文翻译：

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算子方程组$$ AX = C $$ AX = C，$$ XB = D $$ XB = D在希尔伯特中的可解性$$ C {{} ^ {*}} $$ C ∗ -modules

在本文中，我们考虑了Hilbert \（C {{} ^ {*}} \）-模块框架下两个算子方程\（AX = C \）和\（XB = D \）的系统的可解性以及Hermitian和正解的存在。我们还提供了此类解决方案的一般形式的公式。