In this paper we derive necessary and sufficient conditions for the nonnegativity of Moore-Penrose inverses of unbounded Gram operators between real Hilbert spaces. These conditions include statements on acuteness of certain closed convex cones. The main result generalizes the existing result for bounded operators [11, Theorem 3.6].
The objective of this paper is to study the nonnegativity of the Moore-Penrose inverse of an operator between real Hilbert spaces. A sufficient condition ensuring this is given in terms of certain spectral property of all positive splittings of the given operator. A partial converse is proved.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.