Strongly subadditive functions

Let f: ℝ+ → ℝ. The subject is the trace inequality Tr f(A) + Tr f(P2AP2) ≦ Tr f(P12AP12) + Tr f(P23AP23), where A is a positive operator, P1; P2; P3 are orthogonal projections such that P1 + P2 + P3 = I, P12 = P1 + P2 and P23 = P2 + P3. There are several examples of functions f satisfying the inequality (called (SSA)) and the case of equality is described.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  D. Petz.  Quantum Information Theory and Quantum Statistics , 2007 .

[3]  Denes Petz,et al.  From quasi-entropy to skew information , 2007 .

[4]  F. Hansen,et al.  Jensen's Operator Inequality , 2002, math/0204049.

[5]  D. Petz,et al.  Markov triplets on CCR-algebras , 2008, Acta Scientiarum Mathematicarum.

[6]  Dénes Petz,et al.  Gaussian Markov triplets approached by block matrices , 2009 .

[7]  O. Bratteli.  Operator Algebras And Quantum Statistical Mechanics , 1979 .

[8]  F. Hansen,et al.  Jensen's inequality for operators and Löwner's theorem , 1982 .