Some Operator and Trace Function Convexity Theorems
نویسندگان
چکیده
We consider trace functions (A,B) 7→ Tr[(ABA)] where A and B are positive n × n matrices and ask when these functions are convex or concave. We also consider operator convexity/concavity of ABA and convexity/concavity of the closely related trace functional Tr[ABAC]. The concavity questions are completely resolved, thereby settling cases left open by Hiai; the convexity questions are settled in many cases. As a consequence, the Audenaert–Datta Rényi entropy conjectures are proved for some cases. Mathematics subject classification numbers: 47A63, 94A17, 15A99
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تاریخ انتشار 2015