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An extension of the Lowner-Heinz inequality (1207.2864v1)
Published 12 Jul 2012 in math.FA and math.OA
Abstract: We extend the celebrated L\"owner--Heinz inequality by showing that if $A, B$ are Hilbert space operators such that $A > B \geq 0$, then Ar - Br \geq ||A||r-(||A||- \frac{1}{||(A-B){-1}||})r > 0 for each $0 < r \leq 1$. As an application we prove that \log A - \log B \geq \log||A||- \log(||A||-\frac{1}{||(A-B){-1}||})>0.
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