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2016 Reverse Young-type inequalities for matrices and operators
Mojtaba Bakherad, Mario Krnic, Mohammad Sal Moslehian
Rocky Mountain J. Math. 46(4): 1089-1105 (2016). DOI: 10.1216/RMJ-2016-46-4-1089


We present some reverse Young-type inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with operator means. More precisely, we show that if $A, B\in {\mathfrak B}(\mathcal {H})$ are positive operators and $r\geq 0$, $A\nabla _{-r}B+2r(A\nabla B-A\sharp B)\leq A\sharp _{-r}B$. We also prove that equality holds if and only if $A=B$. In addition, we establish several reverse Young-type inequalities involving trace, determinant and singular values. In particular, we show that if $A$ and $B$ are positive definite matrices and $r\geq 0$, then $\label {reverse_trace} \mbox {tr\,}((1+r)A-rB)\leq \mbox {tr}|A^{1+r}B^{-r} |-r( \sqrt {\mbox {tr\,} A} - \sqrt {\mbox {tr} B})^{2}$.


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Mojtaba Bakherad. Mario Krnic. Mohammad Sal Moslehian. "Reverse Young-type inequalities for matrices and operators." Rocky Mountain J. Math. 46 (4) 1089 - 1105, 2016.


Published: 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1352.15023
MathSciNet: MR3563176
Digital Object Identifier: 10.1216/RMJ-2016-46-4-1089

Primary: 15A60 , 47A30 , 47A60

Keywords: determinant , operator mean , positive operator , Trace , ‎unitarily invariant norm , Young inequality

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium


Vol.46 • No. 4 • 2016
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