Relative operator entropies and Tsallis relative operator entropies in JB-algebras

Shuzhou Wang, Zhenhua Wang

Published 2020-12-25Version 1

In this paper, we initiate the study of relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras. We show that the operator inequalities on relative operator entropies and Tsallis relative operator entropies still hold in our settings. In addition, we improve the lower and upper bounds of the relative operator $(\alpha, \beta)$-entropy established by Nikoufar which refined the bounds for the relative operator entropy obtained earlier by Fujii and Kamei.