Generalized Schur complements and oblique projections Original Research Article

Let image be a closed subspace of a Hilbert space image and A a bounded linear selfadjoint operator on image . In this note, we show that the existence of A-selfadjoint projections with range image is related to some properties of shorted operators, Schur complements (in Andoʹs generalization of the classical concept) and compressions.