Weighted CMP inverse of an operator between Hilbert spaces

The purpose of this paper is to study a new generalized inverse called weighted CMP inverse associated with an operator between two Hilbert spaces, using its Wg-Drazin inverse and its Moore-Penrose inverse. This generalized inverse extends the notion of the weighted CMP inverse for a rectangular matrix. We give some new properties of weighted CMP inverse establishing matrix expression for the weighted CMP inverse of an operator and matrix expression for the Moore-Penrose inverse of this new inverse. Applying these results, we introduce and characterize the CMP inverse for a Hilbert space operator.