Sharp bounds for the Tsallis relative operator entropy

Ismail Nikoufar; Mehdi Kanani Arpatapeh

doi:10.1216/rmj.2022.52.1461

Abstract

We give the sharp and refined bounds for the Tsallis relative operator entropy by using the improved Hermite–Hadamard inequality. As an application of our result, we give new bounds for the generalized relative operator entropy. We refine the bounds of the relative operator entropy announced by Fujii and Kamei and provide the precise and sharp bounds.

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Ismail Nikoufar. Mehdi Kanani Arpatapeh. "Sharp bounds for the Tsallis relative operator entropy." Rocky Mountain J. Math. 52 (4) 1461 - 1471, August 2022. https://doi.org/10.1216/rmj.2022.52.1461

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Received: 4 August 2021; Revised: 30 October 2021; Accepted: 2 December 2021; Published: August 2022

First available in Project Euclid: 26 September 2022

MathSciNet: MR4489171

zbMATH: 1511.47020

Digital Object Identifier: 10.1216/rmj.2022.52.1461

Subjects:

Primary: 15A39 , 47A63 , 81P45

Secondary: 15A42 , 81R15

Keywords: noncommutative perspective , Operator inequalities , p-power operator mean , relative operator entropy , Tsallis relative operator entropy

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