Sums of Hermitian Squares as an Approach to the BMV Conjecture
| dc.creator | Burgdorf, Sabine | |
| dc.date | 2008-02-08 | |
| dc.date | 2009-05-20 | |
| dc.date.accessioned | 2026-07-07T13:16:13Z | |
| dc.date.available | 2026-07-07T13:16:13Z | |
| dc.description | Lieb 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.description | 9 pages, grammatical corrections, typos added, new references | |
| dc.identifier | https://arxiv.org/abs/0802.1153 | |
| dc.identifier | http://arxiv.org/abs/0802.1153 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230720 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.subject | Operator Algebras | |
| dc.subject | 11E25; 13J30; 15A90; 15A45 | |
| dc.title | Sums of Hermitian Squares as an Approach to the BMV Conjecture | |
| dc.type | text |