Linear and Multilinear Algebra, ( ISI ), Volume (69), No (9), Year (2019-7) , Pages (1694-1704)

Title : ( Variants of Ando–Hiai inequality for operator power means )

Authors: Mohsen Kian , Mohammad Sal Moslehian , Yuki Seo ,

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‎It is known that for every $t\\\\in (0,1]$ and every $k$-tuple of positive invertible operators ${\\\\Bbb A}=(A_1,\\\\ldots,A_k)$‎ , ‎the Ando--Hiai type inequality for operator power means‎ ‎\\\\[‎ ‎\\\\NORM{P_{\\\\frac{t}{r}}(\\\\omega; {\\\\Bbb A}^r)} \\\\leq \\\\NORM{P_t(\\\\omega; {\\\\Bbb A})^r} \\\\qquad \\\\mbox{for all $r\\\\geq 1$}‎ ‎\\\\]‎ ‎holds‎, ‎where $\\\\NORM{\\\\cdot}$ is the operator norm and $P_{t}(\\\\omega; {\\\\Bbb A})$ is the operator power mean‎. ‎However it is not known any relation between $P_t(\\\\omega; {\\\\Bbb A}^r)$ and $P_t(\\\\omega; {\\\\Bbb A})^r$ under the L\\\\\\\"{o}wner partial order‎. ‎In this paper‎, ‎we present some Ando--Hiai type inequalities for operator power means‎, ‎which give a relation between $P_t(\\\\omega;\\\\Phi(\\\\mathbb{A}^r))$ and $\\\\Phi\\\\left(P_t(\\\\omega;\\\\mathbb{A})^r \\\\right)$ for every unital positive linear map $\\\\Phi$‎. ‎In addition‎, ‎we obtain a difference counterpart to the information monotonicity‎.


, Operator power means; Ando, , Hiai inequality; positive operator.
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author = {محسن کیان and Sal Moslehian, Mohammad and Yuki Seo},
title = {Variants of Ando–Hiai inequality for operator power means},
journal = {Linear and Multilinear Algebra},
year = {2019},
volume = {69},
number = {9},
month = {July},
issn = {0308-1087},
pages = {1694--1704},
numpages = {10},
keywords = {Operator power means; Ando--Hiai inequality; positive operator.},


%0 Journal Article
%T Variants of Ando–Hiai inequality for operator power means
%A محسن کیان
%A Sal Moslehian, Mohammad
%A Yuki Seo
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2019