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arXiv · 1001.3679

The truncated tracial moment problem

Sabine Burgdorf·Igor Klep
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Abstract

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

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Sabine Burgdorf, Igor Klep. 2010-01-20. The truncated tracial moment problem. https://arxiv.org/abs/1001.3679

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