Loewner ordering

Let H be a Hilbert spaceMathworldPlanetmath, and let X,YSym(E) be symmetric operators on H.

We define the Loewner order <F on Sym(E) by declaring X<FY if X-Y is a positive semidefinite invertiblePlanetmathPlanetmath bounded operatorMathworldPlanetmathPlanetmath on H, and X<FY if X-Y is a positive semidefinite invertible bounded operator on H.

Title Loewner ordering
Canonical name LoewnerOrdering
Date of creation 2013-03-22 14:40:15
Last modified on 2013-03-22 14:40:15
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 4
Author mathcam (2727)
Entry type Definition
Classification msc 40A30
Defines Loewner order