Abstract
Abstract The aim of this paper is to present the weighted generalized Moore–Penrose inverse of an operator between two Hilbert spaces as an extension of the Moore–Penrose inverse and the generalized Moore–Penrose inverse defined for an operator on a Hilbert space. Basic properties, characterizations and representations of the weighted generalized Moore–Penrose inverses are established. We extend some known results and give several new results for the generalized Moore–Penrose inverse. Applying the weighted generalized Moore–Penrose inverse, the solvability of some linear equations as well as general solution forms are obtained.
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