Sabine Burgdorf (Author), Igor Klep (Author)

Abstract

V članku podamo nekomutativno različico klasičnega Hilbertovega izreka o pozitivnih polinomih stopnje 4 v 2 spremenljivkah: nekomutativni polinom takšnega tipa, ki ima pozitivno sled, je vsota štirih hermitskih kvadratov in komutatorjev. S pomočjo dualnosti ta rezultat uporabimo za študij problema momentov s sledjo.

Keywords

matematika;nekomutativni polinom;sled;vsota hermitskih kvadratov;problem momentov;prosta pozitivnost;mathematics;noncommutative polynomial;trace;sum of hermitian squares;(truncated) moment problem;free positivity;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 512.623.562.2
COBISS: 15655513 Link will open in a new window
ISSN: 1631-073X
Views: 241
Downloads: 30
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Other data

Secondary title: Polynômes avec une trace positive et le problème quartique des moments traciaux
Secondary abstract: The tracial analog of Hilbert's classical result on positive binary quartics is presented: a trace-positive bivariate noncommutative polynomial of degree at most four is a sum of hermitian squares and commutators. This is applied via duality to investigate the truncated tracial moment problem: a sequence of real numbers indexed by words of degree four in two noncommuting variables with values invariant under cyclic permutations of the indexes, can be represented with tracial moments of matrices if the corresponding moment matrix is positive definite. Understanding trace-positive polynomials and the tracial moment problem is one of the approaches to Connes' embedding conjecture.
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 721-726
Volume: Vol. 348
Issue: fasc. 13-14
Chronology: 2010
ID: 1475205