Sums of Hermitian Squares as an Approach to the BMV Conjecture

dc.creatorBurgdorf, Sabine
dc.date2008-02-08
dc.date2009-05-20
dc.date.accessioned2026-07-07T13:16:13Z
dc.date.available2026-07-07T13:16:13Z
dc.descriptionLieb and Seiringer stated in their reformulation of the Bessis-Moussa-Villani (BMV) conjecture that all coefficients of the polynomial p(t)=Tr[(A+tB)^m], where A and B are positive semidefinite matrices of the same size and m an arbitrary integer, are nonnegative. The coefficient of t^k is the trace of S_{m,k}(A,B), which is the sum of all words of length m in the letters A and B in which B appears exactly k times. We consider the case k=4 and show that S_{m,4}(A,B) is a sum of hermitian squares and commutators. In particular, the trace of S_{m,4}(A,B) is nonnegative.
dc.description9 pages, grammatical corrections, typos added, new references
dc.identifierhttps://arxiv.org/abs/0802.1153
dc.identifierhttp://arxiv.org/abs/0802.1153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230720
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.subjectOperator Algebras
dc.subject11E25; 13J30; 15A90; 15A45
dc.titleSums of Hermitian Squares as an Approach to the BMV Conjecture
dc.typetext

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