Inequalities for Relative Operator Entropies and Operator Means

Abstract

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.

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Acknowledgements

The authors thank anonymous referees for giving valuable comments and suggestions to improve our manuscript.

Funding

The first author was partially supported by JSPS KAKENHI grant number 16K05257.

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Correspondence to Shigeru Furuichi.

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Furuichi, S., Minculete, N. Inequalities for Relative Operator Entropies and Operator Means. Acta Math Vietnam 43, 607–618 (2018). https://doi.org/10.1007/s40306-018-0250-7

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Keywords

  • Operator inequality
  • Positive operator
  • Hermite-Hadamard inequality
  • Operator mean
  • Generalized relative operator entropy
  • Tsallis relative operator entropy

Mathematics Subject Classification (2010)

  • 47A63
  • 47A64
  • 94A17