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math.OA2007★ 63 cited
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
Eric A. Carlen, Elliott H. Lieb
We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is Φ_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j…
math.OA2007
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy
Eric A. Carlen, Elliott H. Lieb
We consider the following trace function on n-tuples of positive operators: Φ_p(A_1,A_2,...,A_n) = Trace (\sum_{j=1}^n A_j^p)^{1/p} and prove that it is jointly concave for 0<p\le…