Weighted MPCEP Inverse of an Operator Between Hilbert Spaces

Abstract

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.