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Improved operator inequalities of some relative operative entropies

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Abstract

In this paper, we investigate the lower and upper bound of the relative operator \((\alpha ,\beta )\)-entropy. We refine and improve the lower and upper bound of the relative operator entropy and generalized relative operator entropy. As a consequence of our result, the bounds of the relative operator entropy announced by Fujii and Kamei will improve.

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Acknowledgements

I would like to thank the referee for the careful reading of the paper and the valuable comments.

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Correspondence to Ismail Nikoufar.

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Nikoufar, I. Improved operator inequalities of some relative operative entropies. Positivity 24, 241–251 (2020). https://doi.org/10.1007/s11117-019-00680-6

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Keywords

  • Operator inequalities
  • Generalized relative operator entropy
  • Operator geometric mean
  • Noncommutative perspective

Mathematics Subject Classification

  • 47A63
  • 81P45
  • 15A39
  • 15A42
  • 81R15