Idempotents related to the weighted Moore-Penrose inverse

Dijana Mosi´c, Dragan Djordjevi´cdjordjevi´c
2011 Functional Analysis, Approximation and Computation   unpublished
We investigate necessary and sufficient conditions for aa † e,f = bb † e,f to hold in rings with involution. Here, a † e,f denotes the weighted Moore-Penrose inverse of a, related to invertible and Hermitian elements e, f ∈ R. Thus, some recent results from [7] are extended to the weighted Moore-Penrose inverse.