caa a22 4500 467891125 CHVBK 20180406152749.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10955-006-9155-2 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9155-2 Hansen Frank Department of Economics, University of Copenhagen, Studiestraede 6, DK-1455, Copenhagen K, Denmark aut Extensions of Lieb's Concavity Theorem [Elektronische Daten] [Frank Hansen] The operator function (A,B)→ Trf(A,B)(K *)K, defined in 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. We obtain, as a special case, a new proof of Lieb's concavity theorem for the function (A,B)→ TrA p K * B q K, where p and q are non-negative numbers with sum p+q ≤ 1. In addition, we prove concavity of the operator function $$(A,B)\to Tr\left[\frac{A}{A+\mu_1}K^*\frac{X1B}{B+\mu_2}K\right]$$ in its natural domain D 2(μ1,μ2), cf. Definition 3. Springer Science + Business Media, Inc., 2006 Lieb's concavity theorem nationallicence operator convex function nationallicence generalized Hessian nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/1(2006-07-01), 87-101 0022-4715 124:1<87 2006 124 10955 https://doi.org/10.1007/s10955-006-9155-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9155-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hansen Frank Department of Economics, University of Copenhagen, Studiestraede 6, DK-1455, Copenhagen K, Denmark aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/1(2006-07-01), 87-101 0022-4715 124:1<87 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer