An extension of the Lowner-Heinz inequality

Mohammad Sal Moslehian, Hamed Najafi

We extend the celebrated Löwner--Heinz inequality by showing that if $A,B$ are Hilbert space operators such that $A>B\ge 0$, then A^r - B^r \geq ||A||^r-(||A||- \frac{1}{||(A-…