# WEIGHTED MOORE-PENROSE INVERSES OF ADJOINTABLE OPERATORS ON INDEFINITE INNER-PRODUCT SPACES

• Qin, Mengjie (Department of Mathematics Shanghai Normal University) ;
• Xu, Qingxiang (Department of Mathematics Shanghai Normal University) ;
• Zamani, Ali (Department of Mathematics Farhangian University)
• Accepted : 2019.08.14
• Published : 2020.05.01

#### Abstract

Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse AMN exists, where A is an adjointable operator between Hilbert C-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses AMN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.

#### Acknowledgement

Supported by : National Natural Science Foundation of China, Shanghai Municipal Science and Technology Commission

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