A characterization of positive semidefinite operators on a Hilbert space
Copyright policy )A characterization of positive semidefinite operators on a Hilbert space
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.
- University of Maryland, Baltimore United States
- University of Maryland, Baltimore County United States
coercive operators, polar cones, Hermitian and normal operators (spectral measures, functional calculus, etc.), 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, Linear operators on ordered spaces, linear complementarity problem, weakly lower semi-continuous functions
coercive operators, polar cones, Hermitian and normal operators (spectral measures, functional calculus, etc.), 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, Linear operators on ordered spaces, linear complementarity problem, weakly lower semi-continuous functions
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