# Löwner’s theorem

A real function $f$ on an interval $I$ is matrix monotone if and only if it is real analytic and has (complex) analytic continuations to the upper and lower half planes such that $\Im(f)>0$ in the upper half plane.

(Löwner 1934)

Title Löwner’s theorem LownersTheorem 2013-03-22 13:34:49 2013-03-22 13:34:49 mathcam (2727) mathcam (2727) 7 mathcam (2727) Theorem msc 40A30