Strong Weighted GDMP Inverse for Operators

Various extensions of DMP-inverses have been proposed recently. Expressions involving G-Drazin inverses and the Moore-Penrose are known as GDMP-inverses. To generalize the definition of the GDMP inverse for square matrices, we firstly present and study the strong weighted G-Drazin inverse for bounded linear operators between two Hilbert spaces. We introduce the strong weighted GDMP inverse and its dual for operators by employing the strong weighted G-Drazin inverse and the Moore-Penrose inverse. Different properties, characterizations and representations for two new inverses are proved. Applying the strong weighted GDMP inverse, we define the strong weighted GDMP partial order.