Linear Algebra and its Applications, ( ISI ), Volume (556), No (6), Year (2018-9) , Pages (220-237)

Title : ( Operator Ky Fan type inequalities )

Authors: S‎. ‎Habibzadeh , J‎. ‎Rooin , Mohammad Sal Moslehian ,

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Abstract

‎In this paper‎, ‎we extend some significant Ky Fan type inequalities in a large setting to operators on Hilbert spaces and derive their equality conditions‎. ‎Among other things‎, ‎we prove that if $f:[0,\infty)\rightarrow[0,\infty)$ is an operator monotone function with $f (1) = 1$‎, ‎$f'(1)=\mu$‎, ‎and associated mean $\sigma$‎, ‎then for all operators $A$ and $B$ on a complex Hilbert space $\mathscr{H}$ such that $0<A,B\leq\frac{1}{2}I$‎, ‎we have‎ ‎\begin{equation*}‎ ‎A'\nabla_\mu B'-A'\sigma B'\leq A\nabla_\mu B-A\sigma B‎, ‎\end{equation*}‎ ‎where $I$ is the identity operator on $\mathscr{H}$‎, ‎$A':=I-A$‎, ‎$B':=I-B$‎, ‎and $\nabla_\mu$ is the $\mu$-weighted arithmetic mean.‎

Keywords

Ky Fan type inequalities; operator mean; operator monotone function; integral representation
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@article{paperid:1069284,
author = {S‎. ‎Habibzadeh and J‎. ‎Rooin and Sal Moslehian, Mohammad},
title = {Operator Ky Fan type inequalities},
journal = {Linear Algebra and its Applications},
year = {2018},
volume = {556},
number = {6},
month = {September},
issn = {0024-3795},
pages = {220--237},
numpages = {17},
keywords = {Ky Fan type inequalities; operator mean; operator monotone function; integral representation},
}

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%0 Journal Article
%T Operator Ky Fan type inequalities
%A S‎. ‎Habibzadeh
%A J‎. ‎Rooin
%A Sal Moslehian, Mohammad
%J Linear Algebra and its Applications
%@ 0024-3795
%D 2018

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