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Operator entropy inequalities

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Moslehian M., Mirzapour F., Morassaei A.

Colloquium Mathematicum

2013

tom 130

nr 2

159-168

We investigate a notion of relative operator entropy, which develops the theory started by J. I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341-348]. For two finite sequences A = (A₁,...,Aₙ) and B = (B₁,...,Bₙ) of positive operators acting on a Hilbert space, a real number q and an operator monotone function f we extend the concept of entropy by setting $S_q^f(A|B): = ∑_{j=1}^{n} A_j^{1/2} (A_j^{-1/2}B_jA_j^{-1/2})^{q} f(A_j^{-1/2}B_jA_j^{-1/2})A_j^{1/2}$, and then give upper and lower bounds for $S_q^f(A|B)$ as an extension of an inequality due to T. Furuta [Linear Algebra Appl. 381 (2004), 219-235] under certain conditions. As an application, some inequalities concerning the classical Shannon entropy are deduced.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Mirzapour F.

1 Morassaei A.

1 Moslehian M.

1 2013

Wyniki wyszukiwania

Operator entropy inequalities