Using compositions of the weighted core–EP inverse and Moore–Penrose inverse, we solve new systems of operator equations and define three new weighted generalized inverses of a bounded linear operator between two Hilbert spaces, which are called the W-MPCEP inverse, W-CEPMP inverse and W-MPCEPMP inverse. The W-MPCEP inverse extends the notion of the MPCEP inverse for an operator. We give operator matrix forms and some characterizations of W-MPCEP, W-CEPMP and W-MPCEPMP inverses. We also establish maximal classes of operators for which the expressions of W-MPCEP, W-CEPMP and W-MPCEPMP inverses are valid.

中文翻译：

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希尔伯特空间之间算子的加权MPCEP逆

利用加权核心EP逆和Moore Penrose逆的组合，我们求解了新的算子方程组，并定义了两个希尔伯特空间之间有界线性算子的三个新的加权广义逆，它们称为W-MPCEP逆，W- CEPMP逆和W-MPCEPMP逆。W-MPCEP逆向运算符扩展了MPCEP逆向的概念。我们给出了算子矩阵形式以及W-MPCEP，W-CEPMP和W-MPCEPMP逆的一些特征。我们还建立了W-MPCEP，W-CEPMP和W-MPCEPMP逆表达式有效的最大算子类别。