Title : ( An extension of the Lowner--Heinz inequality )
Authors: Mohammad Sal Moslehian , Hamed Najafi ,
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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 begin{eqnarray*} A^r - B^r geq ||A||^r- left(||A||- frac{1}{||(A-B)^{-1}||} right)^r > 0 end{eqnarray*} for each 0 < r leq 1 . As an application we prove that begin{eqnarray*} log A - log B geq log||A||- log left(||A||- frac{1}{||(A-B)^{-1}||}\\\\right)>0. end{eqnarray*}
Keywords
, L owner, , Heinz inequality; positive operator; Operator monotone function
@article{paperid:1028015,
author = {Sal Moslehian, Mohammad and Najafi, Hamed},
title = {An extension of the Lowner--Heinz inequality},
journal = {Linear Algebra and its Applications},
year = {2012},
month = {June},
issn = {0024-3795},
keywords = {L owner--Heinz inequality; positive operator; Operator
monotone function},
}
%0 Journal Article
%T An extension of the Lowner--Heinz inequality
%A Sal Moslehian, Mohammad
%A Najafi, Hamed
%J Linear Algebra and its Applications
%@ 0024-3795
%D 2012
