In this talk we present a relation between generalized entropies and operator means. For example, as pointed by Furuichi \cite{SF11}, two upper bounds on the Tsallis entropies suggest the following inequality: for positive operators X and Y and \nu\in[0,1], Tr(X#_\nu Y)\geq 1/2 Tr(X+Y-|X-Y|), where the symbole stands for the weighted geometric mean , that is, X^{1/2}(X^{-1/2}YX^{-1/2})^\nu X^{1/2}. Unfortunately, this inequality does not hold in general, but this is true when XY + YX \geq 0. We can extend this inequality for a general operator mean and it is called the generalized reverse Cauchy inequality. We also give a formulation of new Rényi relative entropies by Mosonyi and Ogawa using operator means.
De Li Gao
De Rolf Gohm
De Aurelian Gheondea
De Ignacio Villanueva
De Michael Brannan
De Douglas Farenick
De David Pérez-García
De Yoshiko Ogata
De Runyao Duan
De Edward Effros
De Hiroyuki Osaka
De Fumio Hiai
De Magdalena Musat
De Nicholas LaRacuente
De Dan Voiculescu
De Aram Harrow
De Seung-Hyeok Kye
De Albert Schwarz
De Amine Marrakchi
De Juan Camilo Arosemena Serrato
De Albert Schwarz
De Juan Camilo Arosemena Serrato
De Francesca Arici
De Amine Marrakchi
