ABSTRACT
We establish a reverse inequality for Tsallis relative operator entropy involving a positive linear map. In addition, we present a converse of Ando's inequality, for each parameter. We give examples to compare our results with the known results by Furuta and Seo. In particular, we establish an extension and a reverse of the Löwner-Heinz inequality under certain conditions. Some interesting consequences in inner product spaces and norm inequalities are also presented.
2010 MATHEMATICS SUBJECT CLASSIFICATIONS:
Acknowledgments
The authors would like to thank the anonymous referees for valuable comments that have been implemented in the final version of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.