Abstract
An adjointable operator acting on a Hilbert $$C^*$$ -module is called a weight if it is self-adjoint and invertible. An indefinite inner-product space as well as weighted projections can be induced by a weight. Some new formulas are provided for weighted Moore–Penrose inverses associated to products and differences of weighted projections. As a result, some characterizations of Moore–Penrose inverses associated to projections are generalized to the weighted case.
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