The invariance of the reverse order law under generalized inverses of the product of two closed range bounded linear operators on Hilbert spaces and characterization of the property by the norm majorization

Abstract EN

In this paper we extend the invariance of the product AC B  under a generalized inverse C  of a matrix C in finite dimensional vector spaces to the Hilbert spaces by using Douglas’s theorem, then we investigate the result and results of the reverse order on Hilbert spaces to study the equivalent conditions for the invariance of the property of the reverse order law for the product of two closed range linear bounded operators on Hilbert spaces.

Then, we characterize the property by the norm majorization.