Editing Positive operator (section)

== Partial order  of  self-adjoint operators  ==
A natural [[partial ordering]] of self-adjoint operators arises from the definition of positive operators. Define <math>B \geq A</math> if the following hold:

# <math>A</math> and <math>B</math> are self-adjoint
# <math>B - A \geq 0</math>

It can be seen that a similar result as the [[Monotone convergence theorem]] holds for [[monotone increasing]], bounded, self-adjoint operators on Hilbert spaces.<ref>Eidelman, Yuli, Vitali D. Milman, and Antonis Tsolomitis. 2004. Functional analysis: an introduction. Providence (R.I.): American mathematical Society.</ref>