# Loewner ordering

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

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