Positive operator

Definition: Given a Hilbert space  ℋ and A ∈ L(ℋ), A is said to be a positive operator if  ⟨Ax, x⟩ ≥ 0 for every x ∈ ℋ.

A positive operator on a complex Hilbert space is necessarily a symmetric operator and has a self-adjoint extension that is also a positive operator.

The set of positive bounded operators on a Hilbert space forms a cone in the algebra of all bounded operators.

Category:Mathematical Structure Category:Linear Algebra

Last modified: 

Monday, October 26, 2015 - 17:56