We establish some new inequalities for K-g-frames in Hilbert \(C^{*}\)-modules using the Moore–Penrose inverse of the adjointable operator K and a parameter \(\lambda \). It turns out that the results which we obtained can lead to some known results if we choose particular values for K and \(\lambda \). We also give a double inequality for K-g-frames in Hilbert \(C^{*}\)-modules with the help of two adjointable operators induced by dual K-g-frame pair.

中文翻译：

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子模块中K -g框架的新不等式

我们使用可邻接算子K的Moore-Penrose逆和参数\（\ lambda \）为Hilbert \（C ^ {*} \）-模块中的K -g帧建立了一些新的不等式。事实证明，如果我们为K和\（\ lambda \）选择特定的值，那么我们获得的结果可能会导致一些已知的结果。我们还借助于两个由双K -g框架对引起的可邻接算子，给出了希尔伯特\（C ^ {*} \）-模块中K -g框架的双重不等式。