A characterization of positive semidefinite operators on a Hilbert space

In this paper, we show that, under certain conditions, a Hilbert space operator is positive semidefinite whenever it is positive semidefinite plus on a closed convex cone and positive semidefinite on the polar cone (with respect to the operator). This result is a generalization of a result by Han and Mangasarian on matrices.This paper was presented at the 90th Annual Meeting of the American Mathematical Society, Louisville, Kentucky, January 25–28, 1984.