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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I would like to thank the referee for the careful reading of the paper and the valuable comments.
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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
- Operator inequalities
- Generalized relative operator entropy
- Operator geometric mean
- Noncommutative perspective
Mathematics Subject Classification