The Truncated Tracial Moment Problem

We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in noncommuting 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 this theory via duality to investigate trace-positive polynomials in noncommuting variables.


Published in:
Journal Of Operator Theory, 68, 1, 141-163
Year:
2012
Publisher:
Bucharest, Theta Foundation
ISSN:
0379-4024
Keywords:
Laboratories:




 Record created 2013-02-27, last modified 2018-03-17


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