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Abstract: We present tracial analogs of the classical results of Curto and Fialkow onmoment matrices. A sequence of real numbers indexed by words in non-commutingvariables with values invariant under cyclic permutations of the indexes, iscalled a tracial sequence. We prove that such a sequence can be representedwith tracial moments of matrices if its corresponding moment matrix is positivesemidefinite and of finite rank. A truncated tracial sequence allows for such arepresentation if and only if one of its extensions admits a flat extension.Finally, we apply the theory via duality to investigate trace-positivepolynomials in non-commuting variables.



Author: Sabine Burgdorf, Igor Klep

Source: https://arxiv.org/



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