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2010

The truncated tracial moment problem

Burgdorf, Sabine, Klep, Igor

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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.

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