Loewner ordering

Let $H$ be a Hilbert space, and let $X,Y\in{\rm Sym}(E)$ be symmetric operators on $H$ .

We define the Loewner order $<_{F}$ on ${\rm Sym}(E)$ by declaring $X<_{F}Y$ if $X-Y$ is a positive semidefinite invertible bounded operator on $H$ , and $X<_{F}Y$ 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