Trace-positive polynomials and the quartic tracial moment problem

Burgdorf, Sabine; Klep, Igor

Trace-positive polynomials and the quartic tracial moment problem

Dateien

269.pdfGröße: 355.7 KBDownloads: 279

Datum

2010

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik
Zukunftskolleg

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

Zusammenfassung

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

nichtkommutative Polynome, Spur, Summen hermitescher Quadrate, noncommutative polynomials, trace, sums of hermitian squares, moment problem

Zitieren

ISO 690

BURGDORF, Sabine, Igor KLEP, 2010. Trace-positive polynomials and the quartic tracial moment problem

BibTex

@techreport{Burgdorf2010Trace-655,
  year={2010},
  series={Konstanzer Schriften in Mathematik},
  title={Trace-positive polynomials and the quartic tracial moment problem},
  number={269},
  author={Burgdorf, Sabine and Klep, Igor}
}

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