A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity

Simple item page
dc.creatorCarlen, Eric A.
dc.creatorLieb, Elliott H.
dc.date2007-10-23
dc.date2007-11-30
dc.date.accessioned2026-07-07T09:22:43Z
dc.date.available2026-07-07T09:22:43Z
dc.descriptionWe revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is Φ_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j=1}^m A_j^p)^{q/p}))^{1/q} for m positive definite operators A_j. In part I we only considered the case q=1 and proved the concavity of Φ_{p,1} for 0 < p \leq 1 and the convexity for p=2. We conjectured the convexity of Φ_{p,1} for 1< p < 2. Here we not only settle the unresolved case of joint convexity for 1 \leq p \leq 2, we are also able to include the parameter q\geq 1 and still retain the convexity. Among other things this leads to a definition of an L^q(L^p) norm for operators when 1 \leq p \leq 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces -- which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.
dc.descriptionProof of a conjecture in math/0701352. Revised version replaces earlier draft. 18 pages, latex
dc.identifierhttps://arxiv.org/abs/0710.4167
dc.identifierhttp://arxiv.org/abs/0710.4167
dc.identifierLett. Math. Phys., Vol. 83, No. 2, pp. 107-126 (2008)
dc.identifierdoi:10.1007/s11005-008-0223-1
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155472
dc.subjectOperator Algebras
dc.subjectMathematical Physics
dc.subject47A63; 15A90
dc.titleA Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
dc.typetext

Files

Collections

arXiv