Weighted weak core inverse of operators
Dijana Mosić, Janko Marovt · Linear and Multilinear Algebra · 2021
As solutions of some operator equations, we present two new outer inverses for bounded linear operators between two Hilbert spaces. Precisely, we introduce and characterize the weighted weak core inverse and the dual weighted weak core inverse. These generalized inverses are extensions of the weak core inverse and its dual which have been recently introduced for complex square matrices. Also, we give various representations for the new inverses including operator matrix representations and the most general form. Applying our results, we define and investigate the weak core inverse and the dual weak core inverse for Hilbert spaces operators.