Convexity of quasi-entropy type functions: Lieb’s and Ando’s convexity theorems revisited
نویسندگان
چکیده
Given a positive function f on (0,∞) and a non-zero real parameter θ, we consider a function Iθ f (A,B,X) = TrX (f(LAR −1 B )RB) −θ(X) in three matrices A,B > 0 and X. This generalizes the notion of monotone metrics on positive definite matrices, and in the literature θ = ±1 has been typical. We investigate how operator monotony of f is sufficient and/or necessary for joint convexity/concavity of Iθ f (A,B,X). Similar discussions are given for quasi-entropies and quantum skew informations. 2010 Mathematics Subject Classification. Primary 81P45; Secondary 54C70.
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تاریخ انتشار 2013