Trace-positive polynomials and the quartic tracial moment problem

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2010
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Konstanzer Schriften in Mathematik; 269
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urn:nbn:de:bsz:352-opus-119770
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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.
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510 Mathematics
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nichtkommutative Polynome,Spur,Summen hermitescher Quadrate,noncommutative polynomials,trace,sums of hermitian squares,moment problem
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ISO 690BURGDORF, 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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