Relative Entropy and Tsallis Entropy of two Accretive Operators

M. Raïssouli, M. S. Moslehian, S. Furuichi

Published 2017-05-19Version 1

Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The present definitions and their related results extend those already introduced in the literature for positive invertible operators.