Extensions of Lieb's concavity theorem

Frank Hansen

研究成果: Article

20 引用 (Scopus)

抜粋

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) → Tr [ A/A+μ 1K*B/B+μ2K] in its natural domain D 212), cf. Definition 3.

元の言語English
ページ(範囲)87-101
ページ数15
ジャーナルJournal of Statistical Physics
124
発行部数1
DOI
出版物ステータスPublished - 2006 7 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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