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

Abstract

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