Inequalities for Relative Operator Entropies and Operator Means
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The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by using the Hermite-Hadamard inequality. We obtain alternative bounds for the Tsallis relative operator entropy and in the process to derive these bounds, we established the significant relation between the Tsallis relative operator entropy and the generalized relative operator entropy. In addition, we study the properties on monotonicity for the weight of operator means and for the parameter of relative operator entropies.
KeywordsOperator inequality Positive operator Hermite-Hadamard inequality Operator mean Generalized relative operator entropy Tsallis relative operator entropy
Mathematics Subject Classification (2010)47A63 47A64 94A17
The authors thank anonymous referees for giving valuable comments and suggestions to improve our manuscript.
The first author was partially supported by JSPS KAKENHI grant number 16K05257.
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