A matrix convexity approach to some celebrated quantum inequalities.
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequalities. A general argument is given using matrix perspectives of operator convex functions. A matrix analogue of Maréchal's extended perspectives provides additional inequalities, including a p + q < or = 1 result of Lieb.
Effros
Edward G
EG
Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA. ege@math.ucla.edu