Extensions of Lieb's concavity theorem
Hansen, Frank
arXiv, 0511090 / Harvested from arXiv
Text on arXiv
The operator function (A,B)\to\tr f(A,B)(K^*)K, defined on pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. As a special case we obtain a new proof of Lieb's concavity theorem for the function (A,B)\to\tr A^pK^*B^{q}K, where p and q are non-negative numbers with sum p+q\le 1. In addition, we prove concavity of the operator function (A,B)\to \tr(A(A+\mu_1)^{-1}K^* B(B+\mu_2)^{-1}K) on its natural domain D_2(\mu_1,\mu_2), cf. Definition 4.1
Publié le : 2005-11-28
Classification:  Mathematical Physics,  Mathematics - Operator Algebras 
@article{0511090,
     author = {Hansen, Frank},
     title = {Extensions of Lieb's concavity theorem},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511090}
}

Hansen, Frank. Extensions of Lieb's concavity theorem. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511090/