A Complementary Inequality to the Information Monotonicity for Tsallis Relative Operator Entropy

We establish a reverse inequality for Tsallis relative operator entropy involving a positive linear map. In addition, we present 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 L\"owner-Heinz inequality under certain condition. Some interesting consequences of inner product spaces and norm inequalities are also presented.