The truncated tracial moment problem (Q2919619)

The authors present tracial analogs of the results previously obtained by R.\,E.\thinspace Curto and L.\,Fialkow for polynomials with real or complex coefficients, in the context of moment matrices. They use the concept of tracial sequence, which are sequences of real numbers indexed by words in noncommuting variables, and whose values are invariant under cyclic permutations of the indices. If the associated moment matrix is positive semidefinite and of finite rank, such a sequence can be represented with tracial moments of matrices. For truncated moment problems, they characterize the existence of such a representation in terms of flat extensions.NEWLINENEWLINE This theory is then applied by the authors to investigate trace-positive polynomials in noncommuting variables.