Open Access
2018 The Quadratic Quantum $f$-Divergence of Convex Functions and Matrices
Silvestru Sever Dragomir
Nihonkai Math. J. 29(1): 1-19 (2018).


In this paper we introduce the concept of quadratic quantum $f$-divergence measure for a continuos function $f$ defined on the positive semi-axis of real numbers, the invertible matrix $T$ and matrix $V$ by $$\mathcal{S}_{f}\left( V,T\right) :=\mathrm{tr}\left[ \left\vert T^{\ast }\right\vert ^{2}f\left( \left\vert VT^{-1}\right\vert ^{2}\right) \right].$$ Some fundamental inequalities for this quantum $f$-divergence in the case of convex functions are established. Applications for particular quantum divergence measures of interest are also provided.


The author would like to thank the anonymous referee for valuable suggestions that have been implemented in the final version of the paper.


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Silvestru Sever Dragomir. "The Quadratic Quantum $f$-Divergence of Convex Functions and Matrices." Nihonkai Math. J. 29 (1) 1 - 19, 2018.


Received: 13 October 2016; Revised: 15 February 2018; Published: 2018
First available in Project Euclid: 6 February 2019

zbMATH: 07063837
MathSciNet: MR3908815

Primary: 47A30 , 47A63
Secondary: 15A60 , 26D10 , 26D15

Keywords: arithmetic mean-geometric mean operator inequality , Convex functions , Operator inequalities , operator perspective , relative operator entropy

Rights: Copyright © 2018 Niigata University, Department of Mathematics

Vol.29 • No. 1 • 2018
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