Abstract

We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341{348]. For two nite sequences A = (A1; : : : ;An) and B = (B1; : : : ;Bn) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting Sf q (AjB) := n Xj=1 A1=2 j (A